Question

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

• 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 B Both assertion and reason are true and reason is not the correct explanation of assertion.

By integrating $a-t$ equation twice, we will get $s-t$ equation.
$a\propto t^n$
$\Rightarrow \frac{dv}{dt}\propto t^n$
On integrating, we get
$\Rightarrow v\propto t^{n+1}$
Further $v=\frac{ds}{dt}$
$\Rightarrow \frac{ds}{dt}\propto t^{n+1}$
On integrating, we get
$s\propto t^{n+2}$
Further

Both assertion and reason are true but reason is not the correct explanation of assertion.