Question

A particle of mass m=5 kg is initially moving in the +x direction with a constant velocity v0=500 m/s. At time t=0, at a position x=0, the particle is suddenly pushed in the -x direction by a constant force of F=-100 N. How far does the particle travel before changing directions? In order words, how far does the particle travel before its instantaneous velocity is 0?

Answer 1

In order to calculate the distance traveled before changing directions, first let's calculate the acceleration using the second law of Newton (let's use a negative force, since it's opposite to the movement):

$\begin{gathered} F=m\cdot a \\ -100=5\cdot a \\ a=-\frac{100}{5}=-20\text{ m/s2} \end{gathered}$

Then, we can calculate the distance traveled using Torricelli's equation:

$\begin{gathered} V^2=V^2_0+2\cdot a\cdot d \\ 0=500^2+2\cdot(-20)\cdot d \\ -40d+250000=0 \\ 40d=250000 \\ d=6250\text{ m} \end{gathered}$

Therefore the particle travels 6250 meters before changing the movement direction.