Question

Equation of motion of a body is $\frac{dv}{dt}=6-3v,$ where $v$ is the velocity in $m{s}^{-1}$ and $t$ is the time in second. Assuming particle at rest initially. Then,

• A. velocity of the body when its acceleration is zero is $2m{s}^{-1}$.
• B. initial acceleration of the body is $6m/s^2$
• C. the velocity of the body when the acceleration is half the initial value is $1m/s$
• D. the body has a uniform acceleration.

Answer 1

Answer: (A), (B), (C)

velocity of the body when its acceleration is zero is $2m{s}^{-1}$.
the velocity of the body when the acceleration is half the initial value is $1m/s$
initial acceleration of the body is $6m/s^2$

$a=\frac{dv}{dt}=6-3v$

therefore when acceleration is zero velocity is $2m/s$

initial acceleration when velocity is zero is $6m/s^2$

velocity of the body when acceleration is $3m/s^2$

$⟹3=6-3v$

$V=1m/s$