# A train decelerates

A train of mass $$m=1.5 \cdot 10^5 kg$$ is travelling at $$40m/s$$ when the brakes are applied and it decelerates steadily. The train travels a distance of $$250m$$ before coming to a halt.

a) Calculate the deceleration of the train.
b) Find the average braking force.

I have tried to solve it using formulas such as:
$$v^2 =v_{0} ^2 +2as$$ and so the others of that family, but they do not work because I need to know three variables to find the others...

## The Attempt at a Solution

A train of mass $$m=1.5 \cdot 10^5 kg$$ is travelling at $$40m/s$$ when the brakes are applied and it decelerates steadily. The train travels a distance of $$250m$$ before coming to a halt.

a) Calculate the deceleration of the train.
b) Find the average braking force.

I have tried to solve it using formulas such as:
$$v^2 =v_{0} ^2 +2as$$ and so the others of that family, but they do not work because I need to know three variables to find the others...

If you read the question carefully, you find you do have 3 variables for that equation. for $$v_{f}^{2} = v_{0}^{2} + 2as$$ you can rearrange( I won't patronise you by asking you to do it) to find $$a$$: $$a = \frac{v_{f}^{2} - v_{0}^{2}}{2s}$$

It is important to remember in problems where something is slowing to a halt, that this implies that your final velocity is 0. this is how you know 3 variables. The same principle applies for something speeding up from rest in which case the initial velocity is 0.

Thank you both for your fast replies. I understood.