Question

A car is travelling at exactly 6 miles per hour and accelerates at a constant rate to exactly 65 miles per hour.

This acceleration takes exactly 14.8 seconds.

What is the rate of acceleration, in miles per hour2?

Answer 1

`14878.04878miles/hours^2`

Explanation:

Let's find a solution by understanding the following:

The acceleration rate is defined as the change of velocity within a time interval, which can be written as:

`A=(Vf-Vi)/T` where:

A=acceleration rate

Vf=final velocity

Vi=initial velocity

T=time required for passing from Vi to Vf.

Using the problem's data we have:

Vf=65miles/hour

Vi=6miles/hour

T=14.8seconds

Using the acceleration rate equation we have:

`A=(65miles/hour - 6miles/hour)/14.8seconds`, but look that velocities use 'hours' unit while 'T' uses 'seconds'.

So we need to transform 14.8seconds into Xhours, as follows:

`X=(14.8seconds)*(1hours/60minutes)*(1minute/60seconds)`

`X=0.0041hours`

Using X=0.0041hours in the previous equation instead of 14.8seconds we have:

`A=(65miles/hour - 6miles/hour)/0.0041hours`

`A=(61miles/hour)/0.0041hours`

`A=(61miles)/(hour*0.0041hours)`

`A=61miles/0.0041hours^2`

`A=14878.04878miles/hours^2`

In conclusion, the acceleration rate is
`14878.04878miles/hours^2`