Question

5.) A car traveling at 15 m/s passes a van that is starting from rest with an acceleration of 3 m/s². (a) How long will it take the van to catch up with the car? (b) How far has the car traveled when the van catches up with it?

Answer 1

As the car moves with the constant speed, the movement can be described by the following equation:

$S = V*t$

As the van moves with the constant acceleration, the movement can be described by the following equation:

$S = V_0 *t + at^2/2$ , where V₀ = 0 (m/s)

If the van catches up with the car then they have travelled the same distance for the same time:

S₁ = S₂; t₁ = t₂

Find time needed to catch up with the car:

$V*t = at^2/2$

$2Vt = at^2$

$at^2-2Vt = 0$

$t(at-2V)=0$

t = 0 -- the moment when the car passes the van;

$at-2V=0$

$at = 2V$

$t = 2V/a$

$t = 2*15/3 = 10 (s)$

Find the distance, the car has travelled when the van catches up with it:

$S = V*t$

$S = 15 * 10 = 150 (m)$

Answer: it takes 10 seconds for the van to catch up with the car; at the moment of catching up the car has travelled 150 m.