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?

Accepted Solution

Answer:[tex]14878.04878miles/hours^2[/tex]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:[tex]A=(Vf-Vi)/T[/tex] where:A=acceleration rateVf=final velocityVi=initial velocityT=time required for passing from Vi to Vf.Using the problem's data we have:Vf=65miles/hourVi=6miles/hourT=14.8secondsUsing the acceleration rate equation we have:[tex]A=(65miles/hour - 6miles/hour)/14.8seconds[/tex], but look that velocities use 'hours' unit while 'T' uses 'seconds'.So we need to transform 14.8seconds into Xhours, as follows:[tex]X=(14.8seconds)*(1hours/60minutes)*(1minute/60seconds)[/tex][tex]X=0.0041hours[/tex]Using X=0.0041hours in the previous equation instead of 14.8seconds we  have:[tex]A=(65miles/hour - 6miles/hour)/0.0041hours[/tex][tex]A=(61miles/hour)/0.0041hours[/tex][tex]A=(61miles)/(hour*0.0041hours)[/tex][tex]A=61miles/0.0041hours^2[/tex][tex]A=14878.04878miles/hours^2[/tex]In conclusion, the acceleration rate is [tex]14878.04878miles/hours^2[/tex]