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

Answer:

$14878.04878miles/hours^2$

Step-by-step 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 $14878.04878miles/hours^2$