Question

Help with the above question and the ones below....

A subway train is traveling at a rate of 22.4 m/s. Brakes are applied and it slows down at a constant rate of 3.5 m/s^2 until it stops at a station. Find the total distance traveled while braking.
72 m
142 m
274 m
163 m

A cyclist is stopped at a traffic light. When the light turns green, the cyclist accelerates at 3.2 m/s^2. After 2.4 seconds, what is the cyclist’s speed?
15 m/s
7.7 m/s
5.6 m/s
0.75 m/s

Answer 1

Train: we're given the initial velocity
`v_0` of 22.4 m/s, told that acceleration
`a` is a constant 3.5 m/s^2, and that it eventually stops so that its final velocity
`v` is 0 m/s. The total distance
`x` can then be computed by solving

`v^2-{v_0}^2=2ax\implies\left(0\,(\mathrm m)/(\mathrm s)\right)^2-\left(22.4\,(\mathrm m)/(\mathrm s)\right)^2=2\left(-3.5\,(\mathrm m)/(\mathrm s^2)\right)x`

`\implies x=71.6\,\mathrm m`

Cyclist: it starts at rest, so
`v_0` is 0 m/s, then it accelerate at a cosntant 3.2 m/s^2, and we're told it does so for 2.4 s. We can solve for
`v` via

`v=v_0+at\implies v=\left(3.2\,(\mathrm m)/(\mathrm s^2)\right)(2.4\,\mathrm s)`

`\implies v=7.7\,(\mathrm m)/(\mathrm s)`

Object: the answer they're looking for here is probably the first choice. But technically any one of these equation can be used to determine the total displacement
`x-x_0`. In order to properly use the other three you need to know the value of
`a_x` which can be computed with the given information, since constant acceleration means average/instantaneous accelerations are the same.