Calculating Time and Displacement for Non-Constant Acceleration

[ItsImpulse]

Homework Statement

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?

Homework Equations

I am not sure how to start other than jerk being the derivative of acceleration

The Attempt at a Solution

Do not know how to form equations at all

 

[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!

 

[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?

 

[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.

 

[ItsImpulse]

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