Each Answer needs 4 significant figures!! A bicycle racer sprints near the end o

Question

Each Answer needs 4 significant figures!!

A bicycle racer sprints near the end of a race to clinch a victory. The racer has an initial velocity of 10.9 m/s and accelerates at the rate of 0.450 m/s2 for 5.13 s. What is his final velocity?
13.2 m/s

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The racer continues at this velocity to the finish line. If he was 319 m from the finish line when he started to accelerate, how much time did he save by accelerating?

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One other racer was 6.70 m ahead when the winner started to accelerate, but he was unable to accelerate, and traveled at a constant speed of 12.4 m/s until the finish line. How far behind (in meters) is he from the winner when the winner crosses the finish line?

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How many more seconds did the other racer takes to cross the finish line?

Explanation / Answer

final velocity v1 = vo + a*t = 10.9+(0.45*5.13) = 13.2 m/s <<<------answer

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distance travelled in t = 5.13s

x = vo*t + 0.5*a*t^2 = (10.9*5.13)+(0.5*0.45*5.13^2) = 61.84 m

position of the racer from the finish line after t time = x1 = 319 -61.84 = 257.16 m

time taken to travel t1 = x1/v1 = 257.16/13.2 = 19.48 s

time taken to finish with acceleration = 5.13+19.48 = 24.61 s

time taken to finish without acceleerating t2 = 319/10.9 = 29.27 s

time saved = 29.27-24.61 = 4.66 s <<<----answer

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other racer

position of the other racer from the finish line = 319-6.7 = 312.3 m

distance by the other racer in 24.61s time = 12.4*24.61 = 305.16 m

racer is 312.3-305.16 = 7.14 m far behind the winner

more seconds reqiured = 7.14/12.4 = 0.5758 s <<<------answer

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