Question

Assertion: In the $v-t$ diagram shown in figure, average velocity between the interval $t=0$ and $t=t_0$ is independent of $t_0$.

Reason: Average velocity in the given interval is $\frac{1}{2}{v}_m$.

• A. Both assertion and reason are true and reason is the correct explanation of assertion.
• B. Both assertion and reason are true and reason is not the correct explanation of assertion.
• C. Assertion is true and reason is false.
• D. Assertion is false and reason is true

Answer 1

The correct option is A Both assertion and reason are true and reason is the correct explanation of assertion.

$\text{Average velocity}=\frac{\text{Displacement}}{\text{Time}}$
$=\frac{\text{Area v-t graph}}{\text{Time}}$
$=\frac{\frac{1}{2}{v}_m{t}_0}{t_0}$
$=\frac{1}{2}{v}_m$
Hence, average velocity between the interval $t=0$ to $t=t_0$ is independent of $t_0$
Both assertion and reason are true and reason is the correct explanation of assertion.