acky, wearing roller-skates, is standing beside his mailbox when his friend Davey skates by at a constant speed of 4m/s. Two seconds later, Jacky skates after his friend and accelerates uniformly at 2m/s. How long does it take Jacky to catch Davey?

Let Jacky takes t seconds to catch up with his friend.

Distance traveled by him can be calculated as follows

s = ut + 1/2 a t²

u = 0, a = 2m / s²

s =.5 x 2 t² = t².

Time during which Davey was in motion is t + 2

Distance covered by him

= 4 (t + 2)

These two distances must be equal due to their meeting.

4 (t + 2) = t²,

t² - 4t - 8 = 0

t = 5.46 s