Question

You are driving your car, and the traffic light ahead turns red. you apply the brakes for 2.26 s, and the velocity of the car decreases to + 5.43 m/s. the carâs deceleration has a magnitude of 2.78 m/s2 during this time. what is the carâs displacement? x =

Answer 1

Let the initial velocity of the car be u.

Final velocity of the car (v) = 5.43 m/s

deceleration (a) = - 2.78 m/s^2

Time taken (t) = 2.26 s

Using the first equation of motion:

v = u + at

u = v - at

$u = 5.43 - (-2.78 \times 2.26)$

u = 5.43 + 6.28

u = 11.71 m/s

Let the car's displacement be x.

Using second equation of motion:

$x = ut + \frac{1}{2}at^2$

$x = 11.71 \times 2.26 - \frac{1}{2} \times 2.78 \times 2.26^2$

x = 26.4646 - 7.0995

x = 19.3651 meters

Hence, the displacement of the car is 19.36 meters