# Jerk equation example

1. Jul 6, 2011

Hi there,

I time (seconds) and speed data for a journey in a car. I looking to get the jerk profile of the car. Jerk can be derived by taking the second derivative of the speed. Can some please show me an example of how to calculate it. Thank you
Some sample data is
Code (Text):

time    speed
1           1
2           3
3           5
4          10
5          15
6           21
7           19
8           18
9           22

2. Jul 6, 2011

### LostConjugate

In order to get the jerk profile for a car, take the number of chrome rims and multiply it by the decibel level of the exhaust.

Sorry I couldn't help myself.

Your looking for the acceleration of the car. So take the difference in speed and divide by the difference in time. For example at time 4 your acceleration is 5 per 1 unit of time^2.

3. Jul 6, 2011

I though jerk is the second derivative of velocity and the first derivative of acceleration? So would I not have to get the derivative of that again. Say the unit for speed is m/s, therefore the acceleration is 5 m/s^2 and is the jerk 5m/s^3?

4. Jul 6, 2011

### danR

You forgot the decibel level of the sound system.

Couldn't help it either.

5. Jul 6, 2011

### LostConjugate

The problem is jerk is not a word in physics. I understand what your saying now. However, if you are traveling at a constant velocity and you accelerate, you will feel a jerk, so jerk is acceleration. Though if you are traveling at a constant acceleration and your acceleration changes you will also feel a jerk. So it can be taken to mean either situation.

6. Jul 6, 2011

### Superstring

Actually, jerk IS a word in physics: http://en.wikipedia.org/wiki/Jerk_(physics)

$$\vec j=\frac {\mathrm{d} \vec a} {\mathrm{d}t}=\frac {\mathrm{d}^2 \vec v} {\mathrm{d}t^2}=\frac {\mathrm{d}^3 \vec x} {\mathrm{d}t^3}$$

Getting back on topic, what I would do is find the average acceleration over the given intervals by taking the change in speed over time, then do the same thing with the acceleration to find the jerk.

ie:

Code (Text):

time    accel
1-2     (3-1)/(2-1)
2-3     (5-3)/(3-2)
3-4     (10-5)/(4-3)
...         ...
...         ...
...         ...
...         ...