Question

The position of an object moving along $x$-axis is given by $x = a + bt^2$, where $a = 8.5 \,m$ and $b = 2.5\, m \,s^{-2}$ and $t$ is measured in seconds. The instantaneous velocity of the object at $t = 2\,s$ is

• A. $5\,m\,s^{-1}$
• B. $10\,m\,s^{-1}$
• C. $15\,m\,s^{-1}$
• D. $20\,m\,s^{-1}$

Answer 1

Answer: (B)

Here, $x = a + bt^2$
Where, $a = 8.5\, m$ and $b = 2.5\, m\, s^{-2}$
Velocity, $v=\frac{dx}{dt}=\frac{d}{dt}\left(a+bt^{2}\right)=2bt$
At $t=2\,s$,
$v = 2\left(2.5\, m\, s^{-2}\right)\left(2 \,s\right) = 10\, m\, s^{-1}$