12583 + Mcqs in Physics Page 243 McqOptions

12101.	A body is thrown vertically upward in air when air resistance is taken into account, the time of ascent is \[{{t}_{1}}\] and time of descent is \[{{t}_{2}}\], then which of the following is true?
A.	\[{{t}_{1}}={{t}_{2}}\]
B.	\[{{t}_{1}}<{{t}_{2}}\]
C.	\[{{t}_{1}}>{{t}_{2}}\]
D.	\[{{t}_{1}}\ge \,\,{{t}_{2}}\]
Answer» C. \[{{t}_{1}}>{{t}_{2}}\]

Discussion

12102.	The velocity v and position r of a body are related as, \[{{v}^{2}}=kr,\] where k is a constant. What will be the velocity after 1 second? Given that the position is zero at \[t=0\].
A.	\[\sqrt{kr}\]
B.	\[k{{r}^{-3/2}}\]
C.	\[\frac{k}{2}{{r}^{0}}\]
D.	cannot be determined from the given information
Answer» D. cannot be determined from the given information

Discussion

12103.	A particle is resting over a smooth horizontal floor. At \[t=0\] a horizontal force starts acting on it. Magnitude of the force increases with time according to law \[G=\alpha t,\] where a is a positive constant and t is time. For the figure shown which of the following statements is/are incorrect?
A.	Curve 1 shows acceleration against time
B.	Curve 2 shows velocity against time
C.	Curve 2 shows velocity against acceleration
D.	none of these
Answer» E.

Discussion

12104.	A body covered a distance of L m along a curved path of a quarter circle. The ratio of distance to displacements
A.	\[\frac{\pi }{2\sqrt{2}}\]
B.	\[\frac{2\sqrt{2}}{\pi }\]
C.	\[\frac{\pi }{\sqrt{2}}\]
D.	\[\frac{\sqrt{2}}{\pi }\]
Answer» B. \[\frac{2\sqrt{2}}{\pi }\]

Discussion

12105.	A body starts with some initial velocity and a constant acceleration. It covers a distance of 200 m in first four second and a distance of 220 m in next two second. The acceleration of the body and its velocity at the end of seventh second are
A.	\[a=5\,m{{s}^{-2}},\,\,\upsilon =75\,m{{s}^{-1}}\]
B.	\[a=7.5\,m{{s}^{-2}},\,\upsilon =100\,m{{s}^{-1}}\]
C.	\[a=20\,m{{s}^{-2}},\,\upsilon =150\,m{{s}^{-1}}\]
D.	\[a=150\,m{{s}^{-2}},\,\upsilon =10\,m{{s}^{-1}}\]
Answer» D. \[a=150\,m{{s}^{-2}},\,\upsilon =10\,m{{s}^{-1}}\]

Discussion

12106.	A point moves in a straight line so that its displacement x metre at time t second is given by \[{{x}^{2}}=1+{{t}^{2}}\]. Its acceleration in \[m{{s}^{2}}\] at time second is
A.	\[\frac{1}{{{x}^{3}}}\]
B.	\[\frac{1}{x}\,-\frac{1}{{{x}^{2}}}\]
C.	\[-\frac{t}{{{x}^{2}}}\]
D.	\[\frac{1}{x}\,-\,\frac{{{t}^{2}}}{{{x}^{3}}}\]
Answer» E.

Discussion

12107.	A train is moving along a straight path with uniform acceleration. Its engine passes across a pole with a velocity of \[60\text{ }km{{h}^{1}}\] and the end (guard's van) passes across same pole with a velocity of \[60\text{ }km{{h}^{1}}\]. The middle point of the train will pass across same pole with a velocity
A.	\[70\text{ }km{{h}^{1}}\]
B.	\[70.7\text{ }km{{h}^{1}}\]
C.	\[65\text{ }km{{h}^{1}}\]
D.	\[75\text{ }km{{h}^{1}}\]
Answer» C. \[65\text{ }km{{h}^{1}}\]

Discussion

12108.	A stone is dropped from a rising balloon at a height of 76 m above the ground and reaches the ground in 6s. What was the velocity of the balloon when the stone was dropped? Take \[g=10\text{ }m/{{s}^{2}}\]
A.	\[\frac{52}{3}\,m/s\] upward
B.	\[\frac{52}{3}\,m/s\] downward
C.	\[3\text{ }m/s\]
D.	\[9.8\text{ }m/s\]
Answer» B. \[\frac{52}{3}\,m/s\] downward

Discussion

12109.	A body dropped from top of a tower fall through 40 m during the last two seconds of its fall. The height of tower is \[(g=10\text{ }m/{{s}^{2}})\]
A.	60 m
B.	45 m
C.	80 m
D.	50 m
Answer» C. 80 m

Discussion

12110.	A stone falls freely under gravity. It covers distances \[{{h}_{1}},\,\,{{h}_{2}}\] and \[{{h}_{3}}\] in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between \[{{h}_{1}},\,\,{{h}_{2}}\] and \[{{h}_{3}}\] is
A.	\[{{h}_{1}}=\frac{{{h}_{2}}}{3}=\frac{{{h}_{3}}}{5}\]
B.	\[{{h}_{2}}=3{{h}_{1}}\text{ }and\text{ }{{h}_{3}}=3{{h}_{2}}\]
C.	\[{{h}_{1}}={{h}_{2}}={{h}_{3}}\]
D.	\[{{h}_{1}}=2{{h}_{2}}=3{{h}_{3}}\]
Answer» B. \[{{h}_{2}}=3{{h}_{1}}\text{ }and\text{ }{{h}_{3}}=3{{h}_{2}}\]

Discussion

12111.	A body A begins to move with initial velocity 2 m/sec and continue to moves at a constant acceleration \[a.\text{ }\Delta \text{t}=10\] seconds after the body A begins to move a body B departs from the same point with an initial velocity 12 m/sec and moves with the same acceleration a. What is the maximum acceleration a at which the body B can overtake A?
A.	\[1\text{ }m/{{s}^{2}}\]
B.	\[2\,m/{{s}^{2}}\]
C.	\[1/2\text{ }m/{{s}^{2}}\]
D.	\[3\text{ }m/{{s}^{2}}\]
Answer» B. \[2\,m/{{s}^{2}}\]

Discussion

12112.	A boat takes 2 hours to travel 8 km and back in Still Water Lake. With water velocity of \[4\,\,km\,\,{{h}^{-1}}\], the time taken for going upstream of 8 km and coming back is
A.	160 minutes
B.	80 minutes
C.	100 minutes
D.	120 minutes
Answer» B. 80 minutes

Discussion

12113.	The distance time graph of a particle at time makes angles \[45{}^\circ \] with the time axis. After one second, it makes angle \[60{}^\circ \] with the time axis. What is the acceleration of the particle?
A.	\[\sqrt{3}-1\]
B.	\[\sqrt{3}+1\]
C.	\[\sqrt{3}\]
D.	1
Answer» B. \[\sqrt{3}+1\]

Discussion

12114.	The graph shown below represent
A.	A and B are moving with same velocity in opposite directions
B.	velocity of B is more than A in same direction
C.	velocity of A is more than B in same direction
D.	velocity of A and B is equal in same direction
Answer» E.

Discussion

12115.	The acceleration of a particle, starting from rest, varies with time according to the relation\[\text{a}=-\text{s}{{\omega }^{2}}\sin \omega \text{t}\]. The displacement of this particle at a time t will be
A.	\[\text{s sin }\omega \text{ t}\]
B.	\[\text{s }\omega \text{ cos }\omega \text{ t}\]
C.	\[\text{s }\omega \text{ sin}\omega \text{t}\]
D.	\[-\frac{1}{2}\left( \text{s}{{\omega }^{2}}\text{ sin }\omega \text{t} \right){{\text{t}}^{2}}\]
Answer» B. \[\text{s }\omega \text{ cos }\omega \text{ t}\]

Discussion

12116.	It is given that \[t=p{{x}^{2}}+qx\], where x is displacement and t is time. The acceleration of particle at origin is
A.	\[-\frac{2\text{p}}{{{\text{q}}^{3}}}\]
B.	\[-\frac{2\text{q}}{{{\text{p}}^{3}}}\]
C.	\[\frac{2\text{p}}{{{\text{q}}^{3}}}\]
D.	\[\frac{2\text{q}}{{{\text{p}}^{3}}}\]
Answer» B. \[-\frac{2\text{q}}{{{\text{p}}^{3}}}\]

Discussion

12117.	The displacement x of a particle along a straight line at time t is given by: \[\text{x = }{{\text{a}}_{\text{0}}}\text{+}\frac{{{\text{a}}_{\text{1}}}\text{t}}{\text{2}}\text{+}\frac{{{\text{a}}_{\text{2}}}}{\text{3}}{{\text{t}}^{\text{2}}}\]. The acceleration of the particle is
A.	\[\frac{{{a}_{2}}}{3}\]
B.	\[\frac{2{{a}_{2}}}{3}\]
C.	\[\frac{{{a}_{1}}}{2}\]
D.	\[{{a}_{0}}+\frac{{{a}_{2}}}{3}\]
Answer» C. \[\frac{{{a}_{1}}}{2}\]

Discussion

12118.	A bus starts moving with acceleration \[2\text{ }m/{{s}^{2}}\]. A cyclist 96 m behind the bus starts simultaneously towards the bus at 20 m/s. After what time will he be able to overtake the bus?
A.	4 sec
B.	8 sec
C.	18 sec
D.	16 sec
Answer» C. 18 sec

Discussion

12119.	A point traversed half of the distance with a velocity \[{{v}_{0}}\]. The half of remaining part of the distance was covered with velocity \[{{v}_{1}}\] and second half of remaining part by \[{{v}_{2}}\] velocity. The mean velocity of the point, averaged over the whole time of motion is
A.	\[\frac{{{\text{v}}_{\text{0}}}\text{+}{{\text{v}}_{1}}+{{\text{v}}_{2}}}{3}\]
B.	\[\frac{\text{2}{{\text{v}}_{\text{0}}}\text{+}{{\text{v}}_{1}}+{{\text{v}}_{2}}}{3}\]
C.	\[\frac{{{\text{v}}_{\text{0}}}\text{+.2}{{\text{v}}_{1}}+2{{\text{v}}_{2}}}{3}\]
D.	\[\frac{{{\text{v}}_{\text{0}}}\text{+2(}{{\text{v}}_{1}}+{{\text{v}}_{2}})}{\text{(2}{{\text{v}}_{\text{0}}}\text{+}{{\text{v}}_{1}}+{{\text{v}}_{2}})}\]
Answer» E.

Discussion

12120.	A bus travelling the first one third distance at a speed of 10 km/h, the next one third at 20 km/h and the last one-third at 60 km/h. The average speed of the bus is
A.	9 km/h
B.	16 km/h
C.	18 km/h
D.	48 km/h
Answer» D. 48 km/h

Discussion

12121.	A man of height h walks in a straight path towards a lamp post of height H with velocity v. Then velocity of the edge of the shadow on the ground will be
A.	\[\frac{hv}{H+h}\]
B.	\[\frac{Hv}{H-h}\]
C.	\[\frac{H+h}{Hv}\]
D.	\[\frac{\left( H-h \right)}{Hh}\]
Answer» C. \[\frac{H+h}{Hv}\]

Discussion

12122.	A 120 m long train is moving in a direction with speed 20 m/s. A train B moving with 30 m/s in the opposite direction and 130 m long crosses the first train in a time [CPMT 1996; Kerala PET 2002]
A.	\[6\,s\]
B.	36 s
C.	38 s
D.	None of these
Answer» E.

Discussion

12123.	Starting from rest, acceleration of a particle is \[a=2(t-1).\] The velocity of the particle at \[t=5s\] is [RPET 2002]
A.	15 m/sec
B.	25 m/sec
C.	5 m/sec
D.	None of these
Answer» B. 25 m/sec

Discussion

12124.	A car, moving with a speed of 50 km/hr, can be stopped by brakes after at least 6m. If the same car is moving at a speed of 100 km/hr, the minimum stopping distance is [AIEEE 2003]
A.	6m
B.	12m
C.	18m
D.	24m
Answer» E.

Discussion

12125.	The velocity of a bullet is reduced from 200m/s to 100m/s while travelling through a wooden block of thickness 10cm. The retardation, assuming it to be uniform, will be [AIIMS 2001]
A.	\[10\times {{10}^{4}}\] m/s2
B.	\[12\times {{10}^{4}}\] m/s2
C.	\[13.5\times {{10}^{4}}\] m/s2
D.	\[15\times {{10}^{4}}\] m/s2
Answer» E.

Discussion

12126.	The motion of a particle is described by the equation \[u=at\]. The distance travelled by the particle in the first 4 seconds [DCE 2000]
A.	\[4a\]
B.	\[12a\]
C.	\[6a\]
D.	\[8a\]
Answer» E.

Discussion

12127.	A body travels for 15 sec starting from rest with constant acceleration. If it travels distances \[{{S}_{1}},\ {{S}_{2}}\] and \[{{S}_{3}}\] in the first five seconds, second five seconds and next five seconds respectively the relation between \[{{S}_{1}},\ {{S}_{2}}\] and \[{{S}_{3}}\] is [AMU (Engg.) 2000]
A.	\[{{S}_{1}}={{S}_{2}}={{S}_{3}}\]
B.	\[5{{S}_{1}}=3{{S}_{2}}={{S}_{3}}\]
C.	\[{{S}_{1}}=\frac{1}{3}{{S}_{2}}=\frac{1}{5}{{S}_{3}}\]
D.	\[{{S}_{1}}=\frac{1}{5}{{S}_{2}}=\frac{1}{3}{{S}_{3}}\]
Answer» D. \[{{S}_{1}}=\frac{1}{5}{{S}_{2}}=\frac{1}{3}{{S}_{3}}\]

Discussion

12128.	What is the relation between displacement, time and acceleration in case of a body having uniform acceleration [DCE 1999]
A.	\[S=ut+\frac{1}{2}f{{t}^{2}}\]
B.	\[S=(u+f)\ t\]
C.	\[S={{v}^{2}}-2fs\]
D.	None of these
Answer» B. \[S=(u+f)\ t\]

Discussion

12129.	An electron starting from rest has a velocity that increases linearly with the time that is \[v=kt,\] where \[k=2m/{{\sec }^{2}}\]. The distance travelled in the first 3 seconds will be [NCERT 1982]
A.	9 \[m\]
B.	16 \[m\]
C.	27 \[m\]
D.	36 \[m\]
Answer» B. 16 \[m\]

Discussion

12130.	A boggy of uniformly moving train is suddenly detached from train and stops after covering some distance. The distance covered by the boggy and distance covered by the train in the same time has relation [RPET 1997]
A.	Both will be equal
B.	First will be half of second
C.	First will be 1/4 of second
D.	No definite ratio
Answer» C. First will be 1/4 of second

Discussion

12131.	A body starts from rest from the origin with an acceleration of \[6\,m/{{s}^{2}}\] along the x-axis and \[8\,m/{{s}^{2}}\] along the y-axis. Its distance from the origin after 4 seconds will be [MP PMT 1999]
A.	56 m
B.	64 m
C.	80 m
D.	128 m
Answer» D. 128 m

Discussion

12132.	The velocity of a body depends on time according to the equation \[v=20+0.1{{t}^{2}}\]. The body is undergoing [MNR 1995; UPSEAT 2000]
A.	Uniform acceleration
B.	Uniform retardation
C.	Non-uniform acceleration
D.	Zero acceleration
Answer» D. Zero acceleration

Discussion

12133.	The initial velocity of the particle is \[10\,\,m/\sec \] and its retardation is \[=8\times \frac{9}{2}=36\ m\]. The distance moved by the particle in \[5th\] second of its motion is [CPMT 1976]
A.	\[1\,\,m\]
B.	\[19\,\,m\]
C.	\[50\,\,m\]
D.	\[75\,m\]
Answer» B. \[19\,\,m\]

Discussion

12134.	When a ball is thrown up vertically with velocity \[{{V}_{o}}\], it reaches a maximum height of 'h'. If one wishes to triple the maximum height then the ball should be thrown with velocity [AIIMS 2005]
A.	\[\sqrt{3}{{V}_{o}}\]
B.	\[3{{V}_{o}}\]
C.	\[9{{V}_{o}}\]
D.	\[3/2{{V}_{o}}\]
Answer» B. \[3{{V}_{o}}\]

Discussion

12135.	A body is thrown vertically upwards. If air resistance is to be taken into account, then the time during which the body rises is [RPET 2000; KCET 2001; DPMT 2001]
A.	Equal to the time of fall
B.	Less than the time of fall
C.	Greater than the time of fall
D.	Twice the time of fall
Answer» C. Greater than the time of fall

Discussion

12136.	From the top of a tower two stones, whose masses are in the ratio 1 : 2 are thrown one straight up with an initial speed u and the second straight down with the same speed u. Then, neglecting air resistance [KCET 2005]
A.	The heavier stone hits the ground with a higher speed
B.	The lighter stone hits the ground with a higher speed
C.	Both the stones will have the same speed when they hit the ground.
D.	The speed can't be determined with the given data.
Answer» D. The speed can't be determined with the given data.

Discussion

12137.	A parachutist after bailing out falls 50 m without friction. When parachute opens, it decelerates at 2 m/s2. He reaches the ground with a speed of 3 m/s. At what height, did he bail out? [AIEEE 2005]
A.	293 m
B.	111 m
C.	91 m
D.	182 m
Answer» B. 111 m

Discussion

12138.	A man drops a ball downside from the roof of a tower of height 400 meters. At the same time another ball is thrown upside with a velocity 50 meter/sec. from the surface of the tower, then they will meet at which height from the surface of the tower [CPMT 2003]
A.	100 meters
B.	320 meters
C.	80 meters
D.	240 meters
Answer» D. 240 meters

Discussion

12139.	A packet is dropped from a balloon which is going upwards with the velocity 12 m/s, the velocity of the packet after 2 seconds will be [Pb PMT 2004]
A.	?12 m/s
B.	12 m/s
C.	?7.6 m/s
D.	7.6 m/s
Answer» D. 7.6 m/s

Discussion

12140.	Three different objects of masses \[{{m}_{1}},{{m}_{2}}\] and \[{{m}_{3}}\] are allowed to fall from rest and from the same point ?O? along three different frictionless paths. The speeds of the three objects, on reaching the ground, will be in the ratio of [AIIMS 2002]
A.	\[{{m}_{1}}:{{m}_{2}}:{{m}_{3}}\]
B.	\[{{m}_{1}}:2{{m}_{2}}:3{{m}_{3}}\]
C.	1 : 1 : 1
D.	\[\frac{1}{{{m}_{1}}}:\frac{1}{{{m}_{2}}}:\frac{1}{{{m}_{3}}}\]
Answer» D. \[\frac{1}{{{m}_{1}}}:\frac{1}{{{m}_{2}}}:\frac{1}{{{m}_{3}}}\]

Discussion

12141.	A body, thrown upwards with some velocity, reaches the maximum height of 20m. Another body with double the mass thrown up, with double initial velocity will reach a maximum height of [KCET 2001]
A.	200 m
B.	16 m
C.	80 m
D.	40 m
Answer» D. 40 m

Discussion

12142.	A body freely falling from the rest has a velocity ?v? after it falls through a height ?h?. The distance it has to fall down for its velocity to become double, is [BHU 1999]
A.	\[2h\]
B.	\[4h\]
C.	\[6h\]
D.	\[8h\]
Answer» C. \[6h\]

Discussion

12143.	A body falling for 2 seconds covers a distance \[S\] equal to that covered in next second. Taking \[g=10\,m/{{s}^{2}},\,S=\] [EAMCET (Engg.) 1995]
A.	30 m
B.	10 m
C.	60 m
D.	20 m
Answer» B. 10 m

Discussion

12144.	A rocket is fired upward from the earth's surface such that it creates an acceleration of 19.6 m/sec2. If after 5 sec its engine is switched off, the maximum height of the rocket from earth's surface would be [MP PET 1995]
A.	245 m
B.	490 m
C.	980 m
D.	735 m
Answer» E.

Discussion

12145.	A body A is projected upwards with a velocity of \[98\,m/s\]. The second body B is projected upwards with the same initial velocity but after 4 sec. Both the bodies will meet after
A.	6 sec
B.	8 sec
C.	10 sec
D.	12 sec
Answer» E.

Discussion

12146.	An aeroplane is moving with horizontal velocity \[u\] at height \[h\]. The velocity of a packet dropped from it on the earth's surface will be (\[g\] is acceleration due to gravity) [MP PET 1995]
A.	\[\sqrt{{{u}^{2}}+2gh}\]
B.	\[\sqrt{2gh}\]
C.	\[2gh\]
D.	\[\sqrt{{{u}^{2}}-2gh}\]
Answer» B. \[\sqrt{2gh}\]

Discussion

12147.	A stone is dropped from a certain height which can reach the ground in 5 second. If the stone is stopped after 3 second of its fall and then allowed to fall again, then the time taken by the stone to reach the ground for the remaining distance is [MNR 1985]
A.	2 sec
B.	3 sec
C.	4 sec
D.	None of these
Answer» D. None of these

Discussion

12148.	A body is slipping from an inclined plane of height \[h\] and length \[l\]. If the angle of inclination is \[\theta \], the time taken by the body to come from the top to the bottom of this inclined plane is
A.	\[\sqrt{\frac{2h}{g}}\]
B.	\[\sqrt{\frac{2l}{g}}\]
C.	\[\frac{1}{\sin \theta }\sqrt{\frac{2h}{g}}\]
D.	\[\sin \theta \sqrt{\frac{2h}{g}}\]
Answer» D. \[\sin \theta \sqrt{\frac{2h}{g}}\]

Discussion

12149.	A mass m slips along the wall of a semispherical surface of radius R. The velocity at the bottom of the surface is [MP PMT 1993]
A.	\[\sqrt{Rg}\]
B.	\[\sqrt{2Rg}\]
C.	\[2\sqrt{\pi Rg}\]
D.	\[\sqrt{\pi Rg}\]
Answer» C. \[2\sqrt{\pi Rg}\]

Discussion

12150.	A ball is thrown from the top of a tower in vertically upward direction. The velocity at a point \[h\]meter below the point of projection is twice of the velocity at a point h meter above the point of projection. Find the maximum height reached by the ball above the top of tower.
A.	\[2h\]
B.	\[3h\]
C.	\[(5/3)h\]
D.	\[(4/3)h\]
Answer» D. \[(4/3)h\]

Discussion

Explore topic-wise MCQs in Joint Entrance Exam - Main (JEE Main).

A body is thrown vertically upward in air when air resistance is taken into account, the time of ascent is \[{{t}_{1}}\] and time of descent is \[{{t}_{2}}\], then which of the following is true?

The velocity v and position r of a body are related as, \[{{v}^{2}}=kr,\] where k is a constant. What will be the velocity after 1 second? Given that the position is zero at \[t=0\].

A particle is resting over a smooth horizontal floor. At \[t=0\] a horizontal force starts acting on it. Magnitude of the force increases with time according to law \[G=\alpha t,\] where a is a positive constant and t is time. For the figure shown which of the following statements is/are incorrect?

A body covered a distance of L m along a curved path of a quarter circle. The ratio of distance to displacements

A body starts with some initial velocity and a constant acceleration. It covers a distance of 200 m in first four second and a distance of 220 m in next two second. The acceleration of the body and its velocity at the end of seventh second are

A point moves in a straight line so that its displacement x metre at time t second is given by \[{{x}^{2}}=1+{{t}^{2}}\]. Its acceleration in \[m{{s}^{2}}\] at time second is

A stone is dropped from a rising balloon at a height of 76 m above the ground and reaches the ground in 6s. What was the velocity of the balloon when the stone was dropped? Take \[g=10\text{ }m/{{s}^{2}}\]

A body dropped from top of a tower fall through 40 m during the last two seconds of its fall. The height of tower is \[(g=10\text{ }m/{{s}^{2}})\]

A stone falls freely under gravity. It covers distances \[{{h}_{1}},\,\,{{h}_{2}}\] and \[{{h}_{3}}\] in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between \[{{h}_{1}},\,\,{{h}_{2}}\] and \[{{h}_{3}}\] is

A boat takes 2 hours to travel 8 km and back in Still Water Lake. With water velocity of \[4\,\,km\,\,{{h}^{-1}}\], the time taken for going upstream of 8 km and coming back is

The distance time graph of a particle at time makes angles \[45{}^\circ \] with the time axis. After one second, it makes angle \[60{}^\circ \] with the time axis. What is the acceleration of the particle?

The graph shown below represent

The acceleration of a particle, starting from rest, varies with time according to the relation\[\text{a}=-\text{s}{{\omega }^{2}}\sin \omega \text{t}\]. The displacement of this particle at a time t will be

It is given that \[t=p{{x}^{2}}+qx\], where x is displacement and t is time. The acceleration of particle at origin is

The displacement x of a particle along a straight line at time t is given by: \[\text{x = }{{\text{a}}_{\text{0}}}\text{+}\frac{{{\text{a}}_{\text{1}}}\text{t}}{\text{2}}\text{+}\frac{{{\text{a}}_{\text{2}}}}{\text{3}}{{\text{t}}^{\text{2}}}\]. The acceleration of the particle is

A bus starts moving with acceleration \[2\text{ }m/{{s}^{2}}\]. A cyclist 96 m behind the bus starts simultaneously towards the bus at 20 m/s. After what time will he be able to overtake the bus?

A point traversed half of the distance with a velocity \[{{v}_{0}}\]. The half of remaining part of the distance was covered with velocity \[{{v}_{1}}\] and second half of remaining part by \[{{v}_{2}}\] velocity. The mean velocity of the point, averaged over the whole time of motion is

A bus travelling the first one third distance at a speed of 10 km/h, the next one third at 20 km/h and the last one-third at 60 km/h. The average speed of the bus is

A man of height h walks in a straight path towards a lamp post of height H with velocity v. Then velocity of the edge of the shadow on the ground will be

A 120 m long train is moving in a direction with speed 20 m/s. A train B moving with 30 m/s in the opposite direction and 130 m long crosses the first train in a time [CPMT 1996; Kerala PET 2002]

Starting from rest, acceleration of a particle is \[a=2(t-1).\] The velocity of the particle at \[t=5s\] is [RPET 2002]

A car, moving with a speed of 50 km/hr, can be stopped by brakes after at least 6m. If the same car is moving at a speed of 100 km/hr, the minimum stopping distance is [AIEEE 2003]

The velocity of a bullet is reduced from 200m/s to 100m/s while travelling through a wooden block of thickness 10cm. The retardation, assuming it to be uniform, will be [AIIMS 2001]

The motion of a particle is described by the equation \[u=at\]. The distance travelled by the particle in the first 4 seconds [DCE 2000]

What is the relation between displacement, time and acceleration in case of a body having uniform acceleration [DCE 1999]

An electron starting from rest has a velocity that increases linearly with the time that is \[v=kt,\] where \[k=2m/{{\sec }^{2}}\]. The distance travelled in the first 3 seconds will be [NCERT 1982]

A boggy of uniformly moving train is suddenly detached from train and stops after covering some distance. The distance covered by the boggy and distance covered by the train in the same time has relation [RPET 1997]

A body starts from rest from the origin with an acceleration of \[6\,m/{{s}^{2}}\] along the x-axis and \[8\,m/{{s}^{2}}\] along the y-axis. Its distance from the origin after 4 seconds will be [MP PMT 1999]

The velocity of a body depends on time according to the equation \[v=20+0.1{{t}^{2}}\]. The body is undergoing [MNR 1995; UPSEAT 2000]

The initial velocity of the particle is \[10\,\,m/\sec \] and its retardation is \[=8\times \frac{9}{2}=36\ m\]. The distance moved by the particle in \[5th\] second of its motion is [CPMT 1976]

When a ball is thrown up vertically with velocity \[{{V}_{o}}\], it reaches a maximum height of 'h'. If one wishes to triple the maximum height then the ball should be thrown with velocity [AIIMS 2005]

A body is thrown vertically upwards. If air resistance is to be taken into account, then the time during which the body rises is [RPET 2000; KCET 2001; DPMT 2001]

From the top of a tower two stones, whose masses are in the ratio 1 : 2 are thrown one straight up with an initial speed u and the second straight down with the same speed u. Then, neglecting air resistance [KCET 2005]

A parachutist after bailing out falls 50 m without friction. When parachute opens, it decelerates at 2 m/s2. He reaches the ground with a speed of 3 m/s. At what height, did he bail out? [AIEEE 2005]

A man drops a ball downside from the roof of a tower of height 400 meters. At the same time another ball is thrown upside with a velocity 50 meter/sec. from the surface of the tower, then they will meet at which height from the surface of the tower [CPMT 2003]

A packet is dropped from a balloon which is going upwards with the velocity 12 m/s, the velocity of the packet after 2 seconds will be [Pb PMT 2004]

Three different objects of masses \[{{m}_{1}},{{m}_{2}}\] and \[{{m}_{3}}\] are allowed to fall from rest and from the same point ?O? along three different frictionless paths. The speeds of the three objects, on reaching the ground, will be in the ratio of [AIIMS 2002]

A body, thrown upwards with some velocity, reaches the maximum height of 20m. Another body with double the mass thrown up, with double initial velocity will reach a maximum height of [KCET 2001]

A body freely falling from the rest has a velocity ?v? after it falls through a height ?h?. The distance it has to fall down for its velocity to become double, is [BHU 1999]

A body falling for 2 seconds covers a distance \[S\] equal to that covered in next second. Taking \[g=10\,m/{{s}^{2}},\,S=\] [EAMCET (Engg.) 1995]

A rocket is fired upward from the earth's surface such that it creates an acceleration of 19.6 m/sec2. If after 5 sec its engine is switched off, the maximum height of the rocket from earth's surface would be [MP PET 1995]

A body A is projected upwards with a velocity of \[98\,m/s\]. The second body B is projected upwards with the same initial velocity but after 4 sec. Both the bodies will meet after

An aeroplane is moving with horizontal velocity \[u\] at height \[h\]. The velocity of a packet dropped from it on the earth's surface will be (\[g\] is acceleration due to gravity) [MP PET 1995]

A stone is dropped from a certain height which can reach the ground in 5 second. If the stone is stopped after 3 second of its fall and then allowed to fall again, then the time taken by the stone to reach the ground for the remaining distance is [MNR 1985]

A body is slipping from an inclined plane of height \[h\] and length \[l\]. If the angle of inclination is \[\theta \], the time taken by the body to come from the top to the bottom of this inclined plane is

A mass m slips along the wall of a semispherical surface of radius R. The velocity at the bottom of the surface is [MP PMT 1993]

A ball is thrown from the top of a tower in vertically upward direction. The velocity at a point \[h\]meter below the point of projection is twice of the velocity at a point h meter above the point of projection. Find the maximum height reached by the ball above the top of tower.