Question

A toy train is pushed forward and released at 2.0m with a speed of 1.0m/s. it rolls at a steady speed for 2.0s, then one wheel begins to stick. the train comes to a stop at 5.0m from the point at which it was released. what is the train's acceleration after its wheel begins to stick?

Answer 1

Recall that

${v_f}^2-{v_0}^2=2a\Delta x$

where

- $v_f$ is the final velocity of the train; 0 in this case, because the train eventually stops

- $v_0$ is the initial velocity of the train; 1.0 m/s in this case, because this initial velocity refers to velocity it starts with after one of the wheels gets stuck, and the train is initially traveling at a constant speed of 1.0 m/s

- $a$ is the acceleration we want to find

- $\Delta x$ is the change in the train's position; 5.0 m in this case

So we have

$-\left(1.0\,\dfrac{\mathrm m}{\mathrm s}\right)^2=2a(5.0\,\mathrm m)$

$\implies a=-0.10\,\dfrac{\mathrm m}{\mathrm s^2}$