A car starts from a certain point at a velocity of 100 kph. After 20 seconds, another car staring from rest, starts at the same point following car A at a uniform acceleration of 3 m/s². Assuming that the road is boundless will car B overtake car A? If yes, where and when?

Answer 1

100,000 meters/3600 seconds = 27.8 m/s

d = 27.8 t

d = (1/2)(3)(t-20)^2
so
18.5 t = t^2 -40 t + 400
solve quadratic for t

Answer 2

Sorry Damon. Gives imaginaries.
x = 27.8(t+20)
x = 1/2(3)t^2
1.5t^2=27.8t+556
1.5t^2 - 27.8t - 556 = 0
Real solutions

Answer 3

d = 27.8 * 20 = 556 m. Head
start.

0.5a*t^2 = 556 + 27.8t.
1.5t^2 = 556 + 27.8t.
1.5t^2 - 27.8t - 556 = 0.

t = Time required for B to catchup.

0.5a*t^2 = Distance at which B catches up.