Physics finding different things?

Question

does anyone know how to do this?...im really confused and don't know how!thanks


A professional race-car driver buys a car that can accelerate at 5.9 m/s(squared). The racer decides to race against another driver in a souped-up stock car. Both start from rest, but the stock-car driver leaves 1.0s before the driver of the sports car. The stock car moves with a constant acceleration of 3.6 m/s(squared).
a)Find the time it takes the sports-car driver to overtake the stock-car driver.
bFind the distance the two drivers travel before they are side by side.
c)Find the velocities of both cars at the instant they are side by side

Answer 1

well the phrase 'overtake' suggests that the distance traveled by the two vehicles is the same.
the equation for distance traveled from rest is
d = 1/2 a t
for the stock car d = 1/2 3.6 t
for the sports car which travels for 1 second less time
d = 1/2 5.9 (t-1)
set those equal to each other and solve for t and there is (a).
plug t back into one of the equations and you get (b).
and v = a t gives you the two car velocities.