Acyclist sprints at the end of a race to clinch a victory. she has an initial velocity of 11.5 m/s and accelerates at a rate of 0.500 m/sâ² for 7.00 s. (a) what is her final velocity? (b) the cyclist continues at this velocity to the finish line. if she is 300 m from the finish line when she starts to accelerate, how much time did she save? (c) the second-place winner was 5.00 m ahead when the winner started to accelerate, but he was unable to accelerate, and traveled at 11.8 m/s until the finish line. what was the difference in finish time in seconds between the winner and runner-up? how far back was the runner-up when the winner crossed the finish line?

a)

b)

c)

Explanation:

For this case we have the following data given:

represent the initial velocity

the time when we have acceleration

the acceleration

represent the distance

the velocity for the second place winner

represent the total distance

Part a

For this case we can use the following equation:

And if we replace we got:

Part b

For this case first let's calculate the time taken to end the race with the initial velocity provided , and if we replace we got:

Now we can find the distance covered whn she accelerates

Now we can calculate the distance for the final velocity:

And the time to complet this distance is:

And the total time would be then:

And we can calculate the tame saved taking the difference from the total tim and

Part c

For this case we have the velocity for the second player;

The total distanc for this case woudl be 300--5 = 295 m we can calculate the time to travel this distance at 11.8 m/s like this:

And if we find the difference between this time and the we got:

And the distance would be: