# Simple Uniform Acceleration Problem

1. May 23, 2008

### TheKovac

1. The problem statement, all variables and given/known data
A bicycles accelerates from rest, covering 16 metres in 4 seconds. The total mass of the bicycle and its rider it 90kg. What is its average acceleration during this time?

2. Relevant equations
x = ut + 0.5at^2
v=xt
a=vt

3. The attempt at a solution
v = x/t
v = (16)/(4)
v = 4 m/s

F = mv/t
F = (90)(4)/4
Fnet = 90N

Fnet = ma
90 = 90a
A= 1 m/s^2 <--WRONG!! - How?
A=2ms <--- RIGHT

2. May 23, 2008

### rock.freak667

Why didn't you just use x = ut + 0.5at^2 ?

3. May 23, 2008

### alphysicist

Your equations are not quite right here and they are leading to some problems. The second and third equations need to be:

$$v_{\rm average} = \frac{x_f-x_i}{\Delta t}$$

$$a_{\rm average} = \frac{v_f-v_i}{\Delta t}$$

This quantity you have calculated is the average velocity over the whole time period.

Dividing the average velocity by the time here does not give you the average acceleration; you would need the beginning and ending velocities.

However, if you use your first equation:

$$\Delta x = v_0 t + \frac{1}{2} a t^2$$

you should get the right answer immediately.

4. Feb 10, 2012

### XGPAT

You can't use a constant acceleration law - The question never said that the acceleration was constant, it wanted you to find the average acceleration.
Also:
average velocity = displacement / time interval
average acceleration = change in velocity / time interval

16/4 = average velocity