Question

A bicycle racer sprints at the end of a race to clinch a victory. The racer has an initial velocity of 13.0 m/s and accelerates at the rate of 0.450 m/s^2 for 7.00 s.

(a) What is his final velocity (in m/s)? 16.15 m/s

(b) The racer continues at this velocity to the finish line. If he was 300 m from the finish line when he started to accelerate, how much time (in s) did he save?

(c) One other racer was 5.00 m ahead when the winner started to accelerate, but he was unable to accelerate and traveled at 13.2 m/s until the finish line. How far ahead of him (in meters and in seconds) did the winner finish?

distance m?

time s?

Answer 1

Given,

Initial velocity, u = 13 m/s

acceleration, a = 0.450 m/s²

time, t = 7 s

(a)

Let final velocity be v

As we know,

=> v = u + at = 13 + (0.450*7) = 13 + 3.15

         = 16.15 m/s

(b)

Distance, d = 300 m

If he was running at constant speed, u = 13 m/s

Time taken would have been, t = 300/13

                                                    = 23.1 s

Now,

if he ran with acceleration 0.450 m/s² for 7 sec

We know,

s = u*t + 1/2*a*t²

=> s = 13*7 + 0.5*0.450*7²

=> s = 91 + 0.225*49 = 91 + 11.025

=> s = 102.025 m

Now,

distance left, d' = 300 - 102.025 = 197.975 m

speed after 7 sec, v = 16.15 m/s

time taken to travel rest of the race, t' = d'/v = 197.975/16.15

                                                               = 12.26 s

total time taken to complete the race, t = 7 +t' = 7 +12.26

                                                                 = 19.26 s

   So,

time saved, t_saved = 23.1 - 19.26

                               = 3.84 s

(c)

Time taken by racer1 to reach finish line is, t = 19.26 s

So,

Speed of racer2, v = 13.2 m/s

Distance traveled by racer2 in 17.67 s, is D = 13.2*19.26

                                                                        = 254.23 m

He was 5 m ahead of racer1, his initial distance from finish line was (300-5) = 295 m

So,

Racer2 was (295-253.23) = 40.77 m behind the finish line when racer1 reached the finish line.

Answer in distance is 40.77 m

Time taken racer2 to complete the race, t' = 295/13.2

                                                                     = 22.35 s

time taken by racer1 is 19.26 s

So, racer1 reached (22.35 - 19.26)= 3.09 s before racer2.

Answer is 3.09 s