Answer to Question #178512 in Physics for Kyle

Question #178512

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.


1
Expert's answer
2021-04-06T13:53:23-0400

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


v1=v01+a1t1,v_1=v_{01}+a_1t_1,t1=v1v01a1=25 ms02.5 ms2=10 s.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:


v2=v02+a2t2,v_2=v_{02}+a_2t_2,t2=v2v02a2=25 ms08 ms2=3.125 s.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:


Δt=t2t1=10 s3.125 s=6.87 s.\Delta t=t_2-t_1=10\ s-3.125\ s=6.87\ s.

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