Question

A train is traveling at a speed of 80km/h when the conductor applies the brakes. The train slows with a constant acceleration of magnitude of 0.5 m/s^2. We want to find the distance the train travels from the time the conductor applies the brakes until the train comes to a complete stop. Which kinematic formula would be most useful to solve for the target unknown?

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Answer 1

d = 493.72 m

Step-by-step explanation:

Given that,

Initial velocity of the train, u = 80 km/h = 22.22 m/s

Acceleration of the train, a = -0.5 m/s² (negative as it slows down)

Finally brakes are applied, v = 0

We need to find the distance the train travels. Let the distance be d. Using third equation of kinematics to find it.

`v^2-u^2=2ad\\\\d=(v^2-u^2)/(2a)\\\\d=(0^2-(22.22)^2)/(2* (-0.5))\\\\d=493.72\ m`

So, the required distance is equal to 493.72 m.