Equation of motion of a body is $\frac{dv}{dt}=-4v+8$ where is velocity in $m/s$ and $t$ is time.

Question

Initial velocity of the particle was zero. Choose the correct options.

OPTIONS

A) Initial rate of change of acceleration is 8

B) The terminal speed is $2\text{m/s}$

C) both A and B

D) Neither A and B

I could find initial acceleration by Substituting $t=0$, with which I get $a=8\text{m/s}^2$.

If I assume terminal velocity to be the point where acceleration is $0$, then $v =2\text{m/s}$.

The right answer is only b, whereas according to my working it’s both a and b. What’s wrong here?

Answer 1

In a) what is asked is the rate of change of acceleration, not the acceleration itself. Rate of change of acceleration is the derivative of acceleration.