A particle moving in a straight line traverses a distance x in time t. If t = x2/2 + x, then which one is correct?

The acceleration of the particle is the cube of its velocity

The retardation of the particle is the cube of its velocity

The acceleration of the particle is the cube of its velocity

The retardation of the particle is the square of its velocity

The acceleration of the particle is the square of its velocity

8 + Mcqs in Calculus Application Velocity 2 in Mathematics Page 1 McqOptions

1.	The distance s of a particle moving along a straight line from a fixed-pointO on the line at time t seconds after start is given by x = (t 1)²(t 2)². What will be the distance of the particle from O when its velocity is zero?
A.	4/27 units
B.	4/23 units
C.	4/25 units
D.	4/35 units
Answer» B. 4/23 units

2.	The distance x of a particle moving along a straight line from a fixed point on the line at time t after start is given by t = ax² + bx + c (a, b, c are positive constants). If v be the velocity of the particle and u( 0) be the initial velocity of the particle then which one is correct?
A.	1/v<sup>2</sup> + 1/u<sup>2</sup> = 4at
B.	1/v<sup>2</sup> + 1/u<sup>2</sup> = -4at
C.	1/v<sup>2</sup> 1/u<sup>2</sup> = 4at
D.	1/v<sup>2</sup> 1/u<sup>2</sup> = -4at
Answer» D. 1/v<sup>2</sup> 1/u<sup>2</sup> = -4at

3.	A particle moves in a horizontal straight line under retardation kv³, where v is the velocity at time t and k is a positive constant. If initial velocity be u and x be the displacement at time,then which one is correct?
A.	1/v<sup>2</sup> = 1/2u<sup>2</sup> + 2kt
B.	1/v<sup>2</sup> = 1/2u<sup>2</sup> 2kt
C.	1/v<sup>2</sup> = 1/u<sup>2</sup> 2kt
D.	1/v<sup>2</sup> = 1/u<sup>2</sup> + 2kt
Answer» E.

4.	A particle moves with uniform acceleration along a straight line and describes distances 21m, 43m and 91m at times 2, 4 and 7 seconds, respectively.What is the velocity of the particle in 3 seconds?
A.	11m/sec
B.	31 cm/sec
C.	21m/sec
D.	41m/sec
Answer» B. 31 cm/sec

5.	A particle moves with uniform acceleration along a straight line and describes distances 21m, 43m and 91m at times 2, 4 and 7 seconds,respectively.What is the distance described by the particle in 3 seconds?
A.	30 cm
B.	31 cm
C.	32 cm
D.	33 cm
Answer» C. 32 cm

6.	A particle moving in a straight line traverses a distance x in time t. If t = x²/2 + x, then which one is correct?
A.	The retardation of the particle is the cube of its velocity
B.	The acceleration of the particle is the cube of its velocity
C.	The retardation of the particle is the square of its velocity
D.	The acceleration of the particle is the square of its velocity
Answer» B. The acceleration of the particle is the cube of its velocity

7.	A particle moves in a straight line and its velocity v at time t seconds is given byv = 3t² 4t + 5 cm/second. What will be the distance travelled by the particle during first 3 seconds after the start?
A.	21 cm
B.	22 cm
C.	23 cm
D.	24 cm
Answer» E.

8.	A particle moves in a straight-line OA; the distance of the particle from O at time t seconds is x ft, where x = a + bt + ct² (a, b > 0). What will be the nature of motion of the particle when c = 0?
A.	Uniform retardation
B.	Uniform speed
C.	Uniform acceleration
D.	Uniform velocity
Answer» E.