# How do you work out average acceleration without time?

1. Dec 4, 2017

### NotVerySmart

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How do you workout average acceleration without time?

I have Initial velocity ,final velocity & distance.

With this I have to workout....

1) Average acceleration

2) Time take to accelerate from initial to final velocity

Regards

Someone a little confused

2. Dec 4, 2017

### haruspex

Since you specify average acceleration, I assume it might not be uniform. If the acceleration profile is unkown then you cannot find the average from just velocities and distance.

This question often comes up in a different form: find average force given mass, initial and final velocities, and distance. The question setter makes the mistake of thinking you can use E=F.s=Δmv2/2, but that only works if F is constant.

E.g. you could try solving the question for two different acceleration profiles and observe that the answers are different. Profiles you could use include constant, SHM over a quarter cycle, a large acceleration for a short time followed by zero acceleration for the remaining distance, etc.

3. Dec 4, 2017

### NotVerySmart

sorry I'm not sure I've helped myself here it does give object mass & frictional force as well.

The actual question I received is below, all practice questions I had before this had time as part of the information given. I found it a lot easier to do them but as this is not the case for this question I have struggled with where to start!

I have searched other forums but with no success of finding a way of calculating this.

A racing car of mass 850 kg accelerates from 20 km/h to 160 km/h over a distance of 300 metres. Frictional forces and wind resistance can be assumed to be 800N.

Determine the following:

(i)The average acceleration

(ii)The time taken to accelerate from 20 km/h to 160km/h

(iii)The tractive force produced by the car to provide this acceleration

(iv)The car finally reaches a speed of 250km/h. Friction and wind resistance are 1800 N at this speed. What power output is required to maintain this speed?

4. Dec 4, 2017

### haruspex

As I posted, you cannot solve that based only on this information. You need to make some assumption about the acceleration profile, i.e. how it changes with time. Section 2 of https://www.physicsforums.com/insights/frequently-made-errors-mechanics-forces/ discusses this in detail in reference to average force.

In the given context, a reasonable assumption would be constant power. With initial speed u, final speed v over distance s and constant power P we find $P=\frac m{3s}(v^3-u^3)$, and we can find average acceleration as $\frac{2P}{m(u+v)}$.
Edit: note that I ignored wind resistance there, so those formulae cannot be applied directly to this problem,

5. Dec 6, 2017

### NotVerySmart

Could you please advise if I'm heading in the right direction or not with the numbers in the image.

Thanks

6. Dec 6, 2017

### haruspex

No, you may have missed the edit I made at the end of post #4. Besides, you should not quote the formula I posted without proof. You need to derive it yourself, but taking into account the given wind resistance.
Start from first principles. If the tractive force provided by the engine at time t is F(t), the drag is D, and the speed is v(t):
- what is the net force?
- what is the acceleration?
- what is the power being provided by the engine?