Question

Two siblings are having a race. Being a good sport the older sibling gives the younger sibling a head start. The younger sibling starts first and runs with a constant velocity of 3m/s. The older sibling starts later and accelerates gradually at a rate of 1m/s2. The older sibling catches the younger one after running for 8s. How much of a head start did the younger sibling get?

I know the answer is 2.6s, but how do you achieve that?

Answer 1

under acceleration, s = 1/2 at^2
at a constant velocity, s = vt
so now just solve for x, the head start distance

1/2 * 1 * 8^2 = 3*8 + x

the answer will be in meters, not seconds
divide that by his speed of 3 m/s, and you get how long he ran to get the head start