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Assertion : If $a=-2 t$ for a particle moving in a straight linestartingwithan initialvelocity $4 \mathrm{~m} / \mathrm{s}$ from the origin, then distance travelled by it in $2 \mathrm{~s}$ is same as displacement.
Reason : Velocity changes direction after $2 \mathrm{~s}$ only.
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Reason : Velocity changes direction after $2 \mathrm{~s}$ only.
Solution:
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The correct answer is:
If both assertion and reason are true but reason is not the correct explanation of assertion.
$a=-2 t$
$\begin{aligned} & \frac{d v}{d t}=-2 t \text { or } \int_4^v d v=-2 \int_0^t t d t \\ & v-4=-t^2 \text { or } v=4-t^2 \\ & \Rightarrow \quad v>0 \text { for } t < 2, \\ & \quad v=0 \text { for } t=2, \\ & v < 0 \text { for } t>2\end{aligned}$
The body reverses its direction of motion after $2 \mathrm{~s}$.
$\begin{aligned} & \frac{d v}{d t}=-2 t \text { or } \int_4^v d v=-2 \int_0^t t d t \\ & v-4=-t^2 \text { or } v=4-t^2 \\ & \Rightarrow \quad v>0 \text { for } t < 2, \\ & \quad v=0 \text { for } t=2, \\ & v < 0 \text { for } t>2\end{aligned}$
The body reverses its direction of motion after $2 \mathrm{~s}$.
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