# Homework Help: Non-Constant Acceleration

1. Jan 21, 2014

### ItsImpulse

1. The problem statement, all variables and given/known data
A car has a constant jerk of 5ms-3 and can only accelerate at a maximum of 2.5ms-2. It can travel at a maximum velocity of 36ms-1. What is the time taken for the car to reach maximum velocity and what is its displacement when it reaches maximum velocity?

2. Relevant equations
I am not sure how to start other than jerk being the derivative of acceleration

3. The attempt at a solution
Do not know how to form equations at all

2. Jan 21, 2014

### vanhees71

Do you know, how to integrate an equation like
$$\frac{\mathrm{d}a}{\mathrm{d} t}=j=\text{const}?$$
That's just using the definition of "jerk" as the derivative of the acceleration wrt. time.

Then think, how is the velocity related to acceleration and displacement with velocity!

3. Jan 21, 2014

### ItsImpulse

Okay so da/dt = 5 and it takes 0.5s to reach maximum acceleration. So would i just integrate 5 with respect to time to get the displacement during that period of time?

4. Jan 21, 2014

### vanhees71

Do it carefully step by step! It's correct to integrate here, of course! So go from the jerk to the acceleration, then to the velocity, and finally to displacement.

5. Jan 21, 2014

### ItsImpulse

Integrate from 0-0.5s then I can use the simple kinematics equations for constant acceleration right? Thank you so much (: