In a 100 m race , the winner crosses the finishing line in 10 s. the runner up takes 10.20 s. Estomate the distance between the winner and runner up as the winner crosses the line. show your method of working . and explain why your answer can only be an estimate.

Since this is a race, both start with initial velocity u = 0, and both cover Distance S = 100m.

For the winner, using S = ut + 1/2at², we get accelaration = 2ms^-2.

Using the same formula for the runner up, we get accelaration a = 1.9157088 ms^-2.

Since at t = 10s, we know that the winner covered exactly 100m,
putting t=10s in the equation S= ut + 1/2at² and substituting the accelaration of the runner up, we can get the distance covered by him in t = 10s,

and hence, S =0.5 * 1.9157088 * 10 * 10 = 95.785440 metres.

Hence the distance between the two is 100 - 95.78544 = 4.21456 m (approx)

This method is only an estimate as we are considering the accelaration to be uniform and other factores such as friction and air resistance, to be negligible.