A cyclist's acceleration

Question

A cyclist is travelling at a velocity of 10m/s when he reaches the top of the slope, which is 80m long. There is a bend at the bottom of the slope, which it would be dangerous to go around any faster than 11 m/s. Because of gravity, if he did not pedal or brake he would accelerate down the slope at 0.1m/s^2. To go as fast as possible but still reach the bottom at a safe speed should the cyclist brake, do nothing or pedal?

Answer 1

$v_t = v_0 + at$

So, $11 = 10 + 0.1t \implies t = 10$. So the time it takes to get to a speed of $11$ m/s from $10$ m/s is $10$ seconds.

Even without any acceleration, distance covered at the initial speed of $10$ m/s in $10$ seconds is $ = 100$ m $\gt 80$ m.

So if the cyclist does nothing, he would cover the distance before reaching the max safe speed of $11$ m/s. Hence it is clear that he should pedal to be as fast as possible and still being at safe speed.