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=-(1)/(4)m^2/s^2=(2m)a`
`\Rightarrow a=-(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.