Q: Two physic students are trying to determine the instantanious speed of a bicycle 5.0m from the start of a 1000m sprint. They use a stopwatch to measure the time taken for the bicycle to cover the first 10m. if the acceleration is constant and the measured time is 4.0s what was the instantanious speen of the bicycle at the 5.0m mark..

no, they say they want to measure his speed 5.0m from the start of a 1000metre sprint. 5 metres from the start could be in either direction (5 metres before or 5 metres after) but it's clear they want to know 5 metres after the start (i.e. 995 metres left go in in the 1000 metre sprint).

They say that the time taken for the bike to cover 10 metres is 4 seconds, so you can subsitute that in to get

Now since the accelleration is constant, you can continue to use those equations of motion to solve at the 5

**metre** mark, using

And then you get 3.5ish m/s

These equations only work with constant accelleration because of the nature of how accelleration works, if its constant, you can easily derive how things will be effected.