Calculating Time and Displacement for Non-Constant Acceleration

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The discussion focuses on calculating the time and displacement for a car experiencing constant jerk while accelerating. The car has a jerk of 5 m/s³, a maximum acceleration of 2.5 m/s², and a top speed of 36 m/s. Participants emphasize the need to integrate jerk to find acceleration, then velocity, and finally displacement. The integration process involves calculating the time to reach maximum acceleration and using kinematic equations for constant acceleration. The conversation highlights the step-by-step approach necessary for solving the problem accurately.
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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
 
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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!
 
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?
 
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.
 
Integrate from 0-0.5s then I can use the simple kinematics equations for constant acceleration right? Thank you so much (:
 
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