Answer to Question #178512 in Physics for Kyle

Question

A school bus and a motorcycle have very different accelerations. The bus can accelerate at a rate of 2.5m/s2 while the motorcycle can accelerate at 8.0m/s2. Assuming both vehicles start from rest and speed up to 25m/s, how much more time will it take the bus to reach that speed than the motorcycle.

Answer 1

Let's first find the time that the bus takes to reach the velocity of 25 m/s:

$$v_1=v_{01}+a_1t_1,$$ $$t_1=\dfrac{v_1-v_{01}}{a_1}=\dfrac{25\ \dfrac{m}{s}-0}{2.5\ \dfrac{m}{s^2}}=10\ s.$$

Then, we can find the time that the motorcycle takes to reach the velocity of 25 m/s:

$$v_2=v_{02}+a_2t_2,$$ $$t_2=\dfrac{v_2-v_{02}}{a_2}=\dfrac{25\ \dfrac{m}{s}-0}{8\ \dfrac{m}{s^2}}=3.125\ s.$$

Finally, we can find the additional time that the bus takes to reach that speed than the motorcycle:

$$\Delta t=t_2-t_1=10\ s-3.125\ s=6.87\ s.$$