The motion of a body is given by the equation \[\frac{dv(t)}{dt}=6.0-3v(t)\]. where \[v(t)\] is speed in \[m/s\] and \[t\] in \[\sec \]. If body was at rest at \[t=0\] [IIT-JEE 1995]

The speed varies with the time as \[v(t)=2(1-{{e}^{-3t}})m/s\]

The terminal speed is 2.0 \[m/s\]

The speed is \[0.1m/s\] when the acceleration is half the initial value

The magnitude of the initial acceleration is \[6.0m/{{s}^{2}}\]

The motion of a body is given by the equation \[\frac{dv(t)}{dt}=6.0-3

1.	The motion of a body is given by the equation \[\frac{dv(t)}{dt}=6.0-3v(t)\]. where \[v(t)\] is speed in \[m/s\] and \[t\] in \[\sec \]. If body was at rest at \[t=0\] [IIT-JEE 1995]
A.	The terminal speed is 2.0 \[m/s\]
B.	The speed varies with the time as \[v(t)=2(1-{{e}^{-3t}})m/s\]
C.	The speed is \[0.1m/s\] when the acceleration is half the initial value
D.	The magnitude of the initial acceleration is \[6.0m/{{s}^{2}}\]
Answer» B. The speed varies with the time as \[v(t)=2(1-{{e}^{-3t}})m/s\]