A car is traveling at a constant speed of 15 m/s on a highway. At the instant this car passes an entrance ramp, a second car enters the highway from the ramp. The second car starts from rest and has a constant acceleration. What acceleration must it maintain, so that the two cars meet for the first time at the next exit, which is 3.0 km away?

Question

aaronq · Answer

How long will the car travelling at constant speed take to get to the ramp?

$\sf \Delta t=\dfrac{\Delta t}{v_o}=\dfrac{3000~m}{15~m/s}=200~s$

This is how long the second car needs to take to cover 3 km form rest:

$\sf \Delta x=v_o\Delta t +\dfrac{1}{2}a_x(\Delta t)^2$

$\sf 3000~m=(0)(200~s) +\dfrac{1}{2}a_x(200~s)^2$

$\sf a_x=\dfrac{2*3000~m}{(200~s)^2}=0.15~m/s^2$