A car starts from rest and travels for 7.0 seconds with auniform

acceleration of + 2.5 m/s^2. The driver then applies thebrakes,

causing a uniform acceleration of - 3.0 m/s^2. If the brakesare

applied for 2.0 seconds, how fast is the car going at the endof the

braking period, and how far has it gone?

Answer

given,

initial speed = 0 m/s

acceleration of + 2.5 m/s^2 for time 7 s.

final velocity after 7 s

using equation of motion

v = u + a t

v = 0 + 2.5 x 7

v = 17.5 m/s

after 7 sec

Brake is applied, uniform acceleration = - 3.0 m/s^2

time = 2 s

speed of the car after 2 s

initial velocity = 17.5 m/s

Again using equation of motion

v = u + a t

v = 17.5 - 3 x 2

v = 11.5 m/s

distance the car has traveled when brake is applied

v² = u² + 2 a s

11.5² = 17.5² - 2 x 3 x s

6 s = 174

s = 29 m

car has moved 29 m after application of the brake.