Question

When jim and rob ride bicycles, jim can only accelerate at three quarters the acceleration of rob. both start from rest at the bottom of a long straight road with constant upward slope. If rob takes 5.7 minutes to reach the top, how much earlier should jim start to reach the top at the same time as rob?

Answer 1

When jim spent t_1 and rob spent t_2 to reach goal, and we put rob's acceleration A, we get\[\frac{1}{2}At_1^2=\frac{1}{2} \cdot \frac{3}{4}At_2^2\]
Then \[t_1=\frac{\sqrt{3}}{2}t_1\].
Therefore we get \[t_2-t_1=\left( 1- \frac{\sqrt{3}}{2} \right) t_2=0.77 s\]