Question

A cart is inially moving at 0.5 m/s along a track with constant fricon. The cart comes to rest aer traveling 1 m. The experiment is repeated on the same track, but now the cart is inially moving at 1 m/s. How far does the cart travel before coming to rest? How can I solve this with a kinematics approach, instead of an energy one

Answer 1

We will have the following:

First, we will write down the information given:

$\begin{cases}v_i=0.5m/s \\ \\ v_f=0m/s \\ \\ d=1m \\ \\ a=\text{?}\end{cases}$

Then from the third kinematic equation:

$v^2_f-v^2_i=2ad$

So:

$(0m/s)^2-(0.5m/s)^2=2(1m)a=-\frac{1}{4}m^2/s^2=(2m)a$$\Rightarrow a=-\frac{1}{8}m/s^2$

So, it's acceleration is -0.125 m/s^2.

Then for the scenario we are interested in:

$\begin{cases}v_i=1m/s \\ \\ v_f=0m/s \\ \\ d= \\ \\ a=-0.125m/s^2\end{cases}$

So:

$(0m/s)^2-(1m/s)^2=2(-0.125m/s^2)d\Rightarrow-1m^2/s^2=(-0.25m/s^2)d$$\Rightarrow d=4m$

So, the cart moved 4 meters.