Modelling a sprinter with a parabolic speed graph

A coach models a sprinter's speed in a \(100\) m race by \(v=kt(10-t)\) m/s for \(0\le t\le10\), where \(t\) is the time in seconds and \(k\) is a positive constant. The sprinter finishes at \(t=10\).

1. Use the fact that the area under the speed–time graph is the distance run to show that \(k=0.6\).[3]
2. Find the time at which the sprinter has run \(50\) m, and explain the answer using the shape of the graph.[2]
3. Find the greatest speed in the model, and give two reasons why the model is not realistic for a real sprinter.[2]