# Acceleration and speed as m*s^-1

1. Jan 23, 2014

### Xecutive

I was given this question today and I have never seen acceleration or speed with a minus power in the unit (m/s^-2). Also speed in the question has a ^-1 in the unit and I thought the unit for speed was m/s (meters per second)

1. The problem statement, all variables and given/known data

A body starts from rest and is subject to a constant contant acceleration of 4ms^-2 up to a speed of 20ms^-1. It then travels 20ms^-1 for 30 seconds after witch time it is retarded to a speed of 4ms^-1, if the complete motion takes 50 seconds, Find:

A) The time taken to reach 20ms^-1.

B) The retardation.

C)Total distance travelled.

2. Relevant equations

3. The attempt at a solution

I have know idea what these strange units mean.

2. Jan 23, 2014

### Staff: Mentor

Hi Xecutive. Welcome to PF!

It is simply standard algebra applied to units (which should be treated as mathematical objects).

$$x^{-1} = \frac{1}{x}$$

$$\mathrm{m} \; \mathrm{s}^{-1} = \frac{\mathrm{m}}{\mathrm{s}}$$

$$\mathrm{m} \; \mathrm{s}^{-2} = \frac{\mathrm{m}}{\mathrm{s}^2}$$

Note that it is not $\mathrm{m} / \mathrm{s}^{-1}$, but $\mathrm{m} \; \mathrm{s}^{-1}$. The former would give
$$\mathrm{m} / \mathrm{s}^{-1} = \frac{\mathrm{m}}{\mathrm{s}^{-1}} = \mathrm{m} \; \mathrm{s}$$

3. Jan 23, 2014

### PhanthomJay

you mean ms^-2 not m/s^-2
yes, the unit for speed is m/s, and m/s can be writen as ms^-1.....it's just taking the denominator, s, and placing it in the numerator as s^-1.
I personally would rather see it written as m/s instead of ms^-1, but they are nevertheless mathematically the same unit, just an algebraic manipulation of the variables.

Welcome to these forums!

4. Jan 23, 2014

### Xecutive

It seems so obvious now.

Thanks.