Question

A person driving a car starts from rest and has a constant acceleration of 2200 miles/hour2

and does so until he reaches 55 mph. The person then drives at that constant speed for 14.5 miles. The

person then slows to a stop at a rate of deceleration of 1575 miles/hour2

. Determine (a) how much total

distance the car has traveled in miles and (b) how much total time in minutes does it take the person to

drive the car from start to finish

Answer 1

Time for accelerating from rest to 55 mph = v/a = 55/2200 = 0.025 hours

Distance travelled from accelerating from rest to 55 mph = 0.5*a*t^2 = 0.5*2200* 0.025^2 = 0.6875 miles.

Distance travelled at constant speed of 55 mph = 14.5 miles

Time required for travelling 14.5 miles at constant speed of 55 mph = 14.5/55 = 0.2636 hours

Time required to slow down to rest from 55 mph with a deceleration of 1575 miles/hour2 = V/ a = 55/1575 = 0.03492 hours

Distance travelled during this time = ut - 0.5*a*t^2 = (55*0.03492) - (0.5*0.03492^2 * 1575) = 0.9603 miles.

a) total distance the car has traveled in miles = 0.6875 + 14.5 + 0.9603 = 16.1478 miles.

b) total time = 0.025 + 0.2636 + 0.03492 = 0.32352 hours = 19.4112 minutes