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Momentum and impulse question

high-speed train with a total mass of 9.25 x 105 kg travels north at a speed of
220km/h. Suppose it takes 16s of constant acceleration for the train to come to rest at a station platform. Calculate the force acting on the train during this time. What is the train's stopping distance?

1 Answer

5 votes

Answer:

So the force acting on the train during the time of constant acceleration is -35,217.75 N and the stopping distance is 985.76 m.

Step-by-step explanation:

The force acting on the train during the time of constant acceleration can be calculated using the equation:

force = mass x acceleration

To calculate the acceleration, we can use the equation:

acceleration = (final velocity - initial velocity) / time

where the final velocity is 0 m/s (the train comes to rest), the initial velocity is 220 km/h (converted to m/s) and the time is 16s.

initial velocity = 220 x 1000/3600 = 61.11 m/s

acceleration = (0 - 61.11) / 16 = -3.819 m/s^2

force = mass x acceleration = 9.25 x 105 kg x -3.819 m/s^2 = -35,217.75 N

The negative sign indicates that the force is acting in the opposite direction of the velocity, which is in the opposite direction of the train's motion, which is braking.

To calculate the stopping distance, we can use the equation:

distance = (initial velocity x time) + (1/2 x acceleration x time^2)

stopping distance = (61.11 m/s x 16s) + (1/2 x -3.819 m/s^2 x 16s^2) = 985.76 m

So the force acting on the train during the time of constant acceleration is -35,217.75 N and the stopping distance is 985.76 m.

User Zach Leighton
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