# Math Help - Finding when the velocity equals x.

1. ## Finding when the velocity equals x.

Hey! I know I've had a lot of questions on here over the past couple days, but I am just ensuring I understand what I am doing, and you guys do such a great job of explaining everything!
Okay, I have a derivative question that I am not entirely sure how to solve, so I was hoping you guys could help me out!

Question
The position function of an object moving along a straight line is given by the function $s(t) = t^3 - 15t^2 + 48t - 10$, where s is in metres and t s in seconds and $0.
i) When is the velocity the object greater than 21 m/s?
ii) When is the speed of the object less than 21 m/s?

Question
I really have no idea how to solve for this! With the equation given I know the distance in metres after t seconds, but not the velocity, and the question is asking for velocity.
How would I go about solving this question?

2. Originally Posted by Kakariki

i) When is the velocity the object greater than 21 m/s?
Find $s'(t)>21$

Originally Posted by Kakariki

ii) When is the speed of the object less than 21 m/s?
Do you mean $\frac{m}{s^2}$ ?

This needs to be confirmed.

I think you are after $s''(t)<21$

3. @pickslides
Speed is the rate of change of distance with time.
Velocity is the rate of change of displacement with time.

which means:

Speed is the first derivative of distance with respect to time.
Velocity is the first derivative of displacement with respect to time.

Let me clarify.

v(t)=s'(t), that is the instantaneous velocity at time t.

Velocity is speed with direction, and speed is velocity with no direction, so the speed equals |v(t)| or |s'(t)|.

What she needs to find is:

i) s'(t)>21

ii)|s'(t)|<21