Question

Assertion: If the acceleration of a particle moving in a straight line varies as $a\propto t^n,$ then its position may vary as $s\propto t^{n+2}$
Reason: If $a–t$ graph is a straight line, then the $s-t$ graph may be a parabola.

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

Answer 1

The correct option is B Both assertion and reason are correct and reason is not the correct explanation of assertion.

By differentiating $s-t$ equation two times, we will get $a-t$ equation.
Thus if $s\propto t^{n+2}$, then $a\propto t^n$
Further, if acceleration is constant, $a-t$ graph is a straight line parallel to time axis. i.e. $a\propto t^0$
In that case, $s\propto t^2$ and $s-t$ graph may be a parabola.