Problem 5 on Motion in a Straight Line

Description:

Problem

A car moving along a straight highway with speed of 126 km/h is brought to a stop within a distance of 200m. What is the retardation of the car (assumed uniform), and how long does it take for the car to stop?

Solution

This is the case of retardation. Therefore,

For the sign convention, assuming the direction of motion of the car to be positive,

Initial velocity of the car, u = 126 km/h = 126 × 1000/3600 = 35 m/s

Final velocity of the car, v = 0 m/s (Car comes to rest)

Displacement of the car, S = 200m

Acceleration is expected to have a negative sign according to the sign convention chosen above.

Also. acceleration is given to be uniform, hence the equations of motion could be applied.

v² = u² + 2aS

0 = (35)² + 2a(200)

a = -3.06 m/s²

S₄ = 19.6 m

To calculate the time taken, we use,

v = u + at

0 = 35 - 3.06 × t

t = 35/3.06 = 11.4 s