Question

Two cars are traveling from the same place and in the same direction. The first car started from rest and speeds up with a constant acceleration of 0.3 m/s^2. The second car leaves 15 seconds after the first car and speeds up with a constant acceleration of 0.5 m/s^2. When will the second car overtake the first car?

Answer 1

$s_0=a_1t^2/2=0.3\cdot15^2/2=33.75(m)$

$v_0=a_1t=0.3\cdot15=4.5(m/s)$

$s_1=s_0+v_0t+a_1t^2/2$

$s_2=a_2t^2/2$

$s_1=s_2\to s_0+v_0t+a_1t^2/2=a_2t^2/2$

$33.75+4.5t+0.3t^2/2=0.5t^2/2$

$0.1t^2-4.5t-33.75=0$ $\to t=51.5(s)$