# Distance Travelled Over Time

1. Nov 16, 2005

### Graham Downs

Hi, all

I have a question that I've been Googling for the past hour or so, and cannot find the answer to. I seem to remember it has something to do with the logarithmic scale. I hope somebody here can answer it for me:

A car accelerates from 0 to 60km/h in 4.2 seconds. What I'd like to know is how far the car has travelled (In metres) after the 4.2 seconds - when it has attained its 60km/h speed.

We cannot assume a constant acceleration, as the speed increases gradually every second of the 4.2 seconds.

Can anybody help with this?

Cheers
Nocturne

Last edited: Nov 16, 2005
2. Nov 16, 2005

### Integral

Staff Emeritus
If we do not assume contant and do not have the rate of acceleration as a function of time there is not a unique answer to the question. The distance traveled is determined by the rate of acceleration.

Assuming a contant acceleration you can use:
$$x = \frac 1 2 a t^2$$ with

$$a = \frac { \Delta v } { \Delta t} = \frac {60 km/h} {4.2 s}$$

You will need to convert the 4.2 seconds to hours.

Last edited: Nov 16, 2005
3. Nov 16, 2005

### Staff: Mentor

You need to know what the acceleration of the car looks like, and that isn't that easy to find without making some pretty big assumptions.