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In a race a distance d long, A and B cross the finish line in a dead heat, both taking a time T. Accelerating uniformly, A takes a time ta and B a time tb to attain maximum speed, which they maintain for the rest of their race.

a) what is the acceleration of each sprinter?

b) what are their respective maximum speeds?

For both questions, express your answer in terms of d, T, ta and tb.

This is what I've done so far.. my logic is probably all wrong but any help is appreciated.

1. First, I think that the equation of A and B will be very similar (only ta, tb and maximum speeds are different).

2. I use the kinematic equations, and divide the race of A into two halves. The first half is when A is accelerating uniformly.

Phase 1

V2 = v1 + a(delta d)^2

V2 = a(delta d)^2

the distance travelled in phase 1 would be (v2 + v1)/2 x ta

d1 = (v2/2)ta

Phase 2

d2 = v2(T - ta)

Can someone tell me if my logic up to this point is correct?