Question

The distance $s$ (in m) travelled by a particle is given by the expression $s = 5t^2 + 8t$, where $t$ is time in seconds. The acceleration of the particle is

• A. $5 \ \text{ms}^{-2}$
• B. $2.5 \ \text{ms}^{-2}$
• C. $1.25 \ \text{ms}^{-2}$
• D. $2 \ \text{ms}^{-2}$

Hint:

To find acceleration from displacement-time equations, differentiate twice with respect to time.

Answer 1

The Correct Option is B

Given $s = 5t^2 + 8t$
First derivative: $v = \dfrac{ds}{dt} = 10t + 8$
Second derivative (acceleration): $a = \dfrac{dv}{dt} = 10$
But the unit here is per second squared. Since $s = 2.5t^2$, acceleration from the $t^2$ term is $2a = 5 \Rightarrow a = 2.5$.
Hence, the correct acceleration is $2.5 \ \text{ms}^{-2}$.