Answer to Question #242753 in Mechanics | Relativity for wewek

Question

A car has an initial velocity of 30 m/s and an acceleration of -5 m/s². Find its displacement when it comes to stop.

Answer 1

We use the information provided and we find first the time (for the car to stop, this occurs when V_f = 0m/s) and then the displacement after substitution for a movement with linear acceleration:

$d_0=0\,m \\ a=-5\frac{m}{s^2} \\ v_i=30\frac{m}{s} \\ v_f=0\frac{m}{s} \\v_f=v_i+at \\ \implies t=\cfrac{v_f-v_i}{a}=\cfrac{(0-30)\frac{m}{s}}{-5\frac{m}{s^2}}=6\,s \\ \text{Now we substitute t=6s and we find:} \\d=d_0+v_0t+\cfrac{at^2}{2} \\d=0\,m+(30\frac{m}{s})(6\,s)+\cfrac{-5\frac{m}{s^2}(6\,s)^2}{2} \\ \implies d=0\,m+180\,m-90\,m=90\,m$

After substitution, we find that the displacement when the vehicle comes to stop is about 90 m.

Reference:

• Sears, F. W., & Zemansky, M. W. (1973). University physics.