Question

Assertion :If the distance traveled by body is directly proportional to the square of time taken, then its speed is increasing with time. Reason: The speed is equal to the time rate of change of distance.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Let $x\left(t\right)$ be the distance covered and $v\left(t\right)$ be the speed at any time $t$.
$x\left(t\right)=k{t}^2$ , where $k$ is some positive constant as distance covered is always positive.
$v\left(t\right)=\frac{dx}{dt}$
$v\left(t\right)=2kt$
Now, $t>0$. Hence, $v\left(t\right)$ is always positive.
Hence, the assertion is correct.
The reason is the correct explanation of the Assertion.