Question

If the displacement of a particle varies with time as $\sqrt{x}=t+7$, which of the following statements is(are) true?

• A. Velocity of the particle is inversely proportional to $t$.
• B. Velocity of the particle is proportional to $t$.
• C. Velocity of the particle is proportional to $\sqrt{t}$.
• D. The particle moves with a constant acceleration.

Answer 1

Answer: (B), (D)

Velocity of the particle is proportional to $t$.
The particle moves with a constant acceleration.

$\sqrt{x}=t+7\Rightarrow x={(t+7)}^2\Rightarrow v=\frac{dx}{dt}=2(t+7)$
Thus, Velocity is proportional to time.
Also as $a=\frac{dv}{dt}=2$
Thus particle moves with a constant acceleration.