Question

A particle starts from $x=0$ and moves along a straight line such that its velocity $v$ depends on position $x$ as $v=x+4$.
Acceleration of the particle at $t=0$ is

• A. $e^{4}m/s^2$
• B. $4e^{4}m/s^2$
• C. $4m/s^2$
• D. $0$

Answer 1

The correct option is C $4m/s^2$

Velocity of the particle, $v=x+4$
Acceleration $a=\frac{dv}{dt}=\frac{d(x+4)}{dt}$
$\Rightarrow a=v=x+4$
At $t=0,x=0$
∴ Acceleration at $t=0\text{is}4m/s^2$