1) An 18-year-old runner can complete a 10.0 km course with an average speed of

Question

1) An 18-year-old runner can complete a 10.0 km course with an average speed of 4.52 m/s. A 50-year-old runner can cover the same distance with an average speed of 4.07 m/s. How much later (in seconds) should the younger runner start in order to finish the the course at the same time as the older runner?
s

2) A sprinter explodes out of the starting block with an acceleration of +3.8 m/s2, which she sustains for 1.4 s. Then, her acceleration drops to zero for the rest of the race.

(a) What is her velocity at t = 1.4 s.

m/s

(b) What is her velocity at the end of the race?

m/s

3) What is the magnitude of the average acceleration of a skier who, starting from rest, reaches a speed of 8.4 m/s when going down a slope for 6.9 s?

m/s2

How far does the skier travel in this time?
m

Explanation / Answer

1)

the delay in starting time of younger runner is the difference in time taken to complete the total distance
time taken by younger runner =(10km)/(4.07m/s)
= 2457 seconds
time taken by older runner =(10km)/(4.52m/s)
= 2212.389 seconds
so difference = 2457 seconds-2212.389 seconds
=244.61 seconds

2)

a)v=at so, answer 1 is 3.8 * 1.4 = 5.32 m/s.

b)After 1.4 seconds acceleration stops and she maintains a constant velocity, so 5.32 m/s is also the velocity at then end of the race.

3)

a) The average acceleration is A = V/T = 8.4/6.9 = 1.21739 m/s^2.

b) The average speed is Vavg = V/2 = 4.2 m/s. In T = 6.9 s, she will have traveled S = Vavg T = 4.

2*6.9 = 28.98 meters.

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