Question

A racing car is traveling along a horizontal track. The car, starting from rest accelerates uniformly at 4.50ms-2 for 15s when it reaches maximum speed. It then travels at this speed for 20s before deceleration uniformly at 5.60ms-2 until it come to rest.

I. Determine the maximum speed reached by the car

Ii. Determine the distance travelled by the car before reaching maximum speed

iii. Determine the time taken for the car to decelerate form it’s maximum speed and comes to rest

iv. Determine the total distance travelled by the car

Answer 1

Given:

$v_0=0$

$a_1=4.50\rm \: m/s^2$

$t_1=15\:\rm s$

$t_2=20\:\rm s$

$a_2=5.60\:\rm m/s^2$

$v_2=0$

i. The maximum speed reached by the car

$$v_1=v_0+a_1t_1=0+4.50*15=67.5\rm \: m/s$$

ii. The distance travelled by the car before reaching maximum speed

$$d_1=v_0t_1+a_1t_1^2/2=0+4.50*15^2/2=506.25\: \rm m$$

iii. The time taken for the car to decelerate form it’s maximum speed and comes to rest

$$t_3=v_1/a_2=67.5/5.60=12\:\rm s$$

iv. The total distance travelled by the car

$$d=d_1+v_1t_2+(v_1+v_2)/2t_3\\ =\rm 506.25+67.5*20+67.5/2*12=2263\: m$$