Question

When you see a traffic light turn red, you apply the brakes until you come to a stop. Suppose your initial speed was 10.6 m/s, and you come to rest in 35.8 m. How much time does this take? Assume constant deceleration.

Answer 1

\[S=V_0·t-\frac{ 1 }{ 2}a·t^2\]\[V=V_0-a·t\]
The time to stop can be calculated when\[ V=0\rightarrow t_s=\frac{ V_0 }{ a }\rightarrow S=\frac{ V_0^2 }{ a}-\frac{ 1 }{ 2}a \left( \frac{ V_0 }{ a} \right)^2\rightarrow a=\frac{ V_0^2 }{ 2S}\]\\[t_s=\frac{ V_0 }{ a}=V_0·\frac{ 2S }{ V_0^2 }=\frac{ 2S }{ V_0}=\frac{ 71.6 }{ 10.6 }=???\]

Answer 2

As acceleration is constant you could have also done (m stands for the mass of the car):
Work to stop the car:
\[E_s=F·S=m·a·S\]
Equals Kinetic Energy of the car:
\[E_K=\frac{ 1 }{ 2 }mV_0^2\]\[E_s=E_K \rightarrow m·a·S=\frac{ 1 }{ 2 }mV_0^2\rightarrow a=\frac{ V_0^2 }{ 2S}\]Again, replace this value in:
\[V=V_0-a·t_s=0\rightarrow t_s=\frac{ V_0 }{a }=V_0\frac{ 2S }{ V^2_0 }=\frac{ 2S }{V_0 }\]

Answer 3

Awesome, thanks so much.