Question

A motorist is traveling at 54 km/h when she observes that a traffic light 240 m ahead of her turns red. The traffic light is timed to stay red for 24 s. If the motorist wishes to pass the light without stopping just as it turns green again, determine: a. The required uniform deceleration of the car, b. The speed of the car as it passes the light.

Answer 1

Given:

u = 54 km/h = 15m/s

s = 240 m

t = 24 s

To find:

1) deceleration a =?

2) speed v =?

Explanation:

1)

The de-acceleration of the car is calculated by the law of kinematics is given by

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

240 = 15 (24) + 0.5 (a) (24)(24)

240 =  360 + 288a

⇒ a = -0.4167 m/$s^2$

- ve sign shows that it is de-acceleration.

∴ a = 0.4167 m/$\mathbf{s^2}$

2)

The speed of motor as it passes the light is calculated by the law of kineamatics is given by

v = u + at

  = 15 + (-0.4167) 24

v = 5m/s

v = 18Km/hr