Question

Kinematics Problem:

A car accelerated from 1.8 mph to some final velocity over 5.8 s. Then, going at this final velocity, the car traveled 8.3 miles over the course of the next 9.1 minutes.

What was acceleration of the car over the first 5.8 s?

Answer 1

consider the motion of the car during travelling 8.3 miles at constant final velocity :

V = constant final velocity of the car = ?

t = time of travel = 9.1 min = 9.1 x 60 = 546 sec

D = distance travelled = 8.3 miles = 8.3 x 1609.34 m = 13357.52 m

using the equation

V = D/t

V = 13357.52/546

V = 24.5 m/s

consider the motion of the car while it accelerates :

V_o = initial velocity of the car = 1.8 mph = 1.8 (miles/hour) (1609.34 m/1 mile) (1 h /3600 sec ) = 0.805 m/s

a = acceleration of the car = ?

t = time taken = 5.8 sec

using the equation

V = V_o + at

24.5 = 0.805 + a (5.8)

a = 4.1 m/s²