Rate of change question involving velocity, displacement and acceleration

Question

I have been having trouble understanding questions c)-e) and am in need of some help:

An object is moving in a straight line from a fixed point. The displacement $s$ in metres is given by $s=-2t^2+28t+45$, $t\geq0$, where $t$ is in seconds.

$a)$ Find the velocity at any time:

$$v(t)=s'(t)=-2t^2+28t+45$$ $$v(t)=-4t+28$$ $$v(1)=-4(1)+28$$ $$v=24m/s$$

$b)$What is the velocity at $t=3s$? $$v(3)=-4(3)+28$$ $$v=16m/s$$

$c)$Find $t$ when the object reaches its maximum displacement:

• Would this be when the velocity is equal to zero, find the critical points, second derivative test for a maximum?

$d)$Find the maximum displacement reached by this object:

• Probably plugging t from $c)$ into the initial function?

$e)$Determine the acceleration at any time:

I believe this is just the second derivative of the initial function or the first derivative of velocity? $$a(t)=v'(t)=-4t+28\\$$ $$a(t)=-4m/s^2$$

Thanks

Answer 1

The answer to part a) is a formula which will give the velocity at time $t$. So, the answer should be $-4t+28$ m/s. I don't belive they are looking for the velocity at an arbitrary time that you choose. Everything else looks fine.