Calculating Time and Displacement for Non-Constant Acceleration

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Homework Help Overview

The problem involves a car experiencing constant jerk and seeks to determine the time taken to reach maximum velocity and the corresponding displacement. The subject area pertains to kinematics and dynamics, particularly focusing on non-constant acceleration due to the presence of jerk.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between jerk, acceleration, and velocity, with one participant questioning how to integrate the jerk to find acceleration. Others explore the integration process and its implications for calculating displacement.

Discussion Status

The discussion is active, with participants offering guidance on integration steps and the relationships between different kinematic quantities. There is a focus on ensuring careful progression through the mathematical relationships involved.

Contextual Notes

Participants note the need to integrate over specific time intervals and consider the use of kinematic equations for constant acceleration, indicating a structured approach to the problem despite some initial uncertainty.

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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
[tex]\frac{\mathrm{d}a}{\mathrm{d} t}=j=\text{const}?[/tex]
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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