Question

When running a 100 meter race Bill reaches his maximum speed when he is 45 meters from the starting line and 5 seconds have elapsed since the start of the race. Bill maintains this maximum (constant) speed for the rest of the race. If Bill is 85 meters from the starting line 10 seconds after the start of the race: a. What is Bill's max speed? meters per second Preview घ7 b. If Bill runs for an additional 3 seconds after reaching his max speed... i. How far will Bill travel during those 3 seconds? meters Preview 11. What is Bill's distance from the starting line 8 seconds after the start of the race? meters Preview c. What is Bill's distance from the starting line 6.5 seconds after the start of the race? meters Preview Submit​

Answer 1

Bill's speed is constant after 5 seconds and 45 meters into the race.

Correct responses:

a. Bill's maximum speed is 8 m/s

b. 24 meters

c. 57 meters

Methods used to calculate speed and distance traveled

Given parameters are;

The distance of the race = 100 meter

Distance at which Bill reaches maximum speed = 45 meters

Speed Bill maintains after 5 seconds = The maximum speed

Time at which Bill is 85 meters from the starting line = 10 seconds after start

a. Required;

Bill's maximum speed in meters.

Solution:

Distance Bill runs at maximum speed, d = 85 m - 45 m = 40 m

Time at which Bill runs the 40 m at maximum speed, t = 10 s - 5 s = 5 s

$Speed = \mathbf{\dfrac{Distance}{Time}}$

Therefore;

• $Bill's \ maximum \ speed = \dfrac{40 \ m}{5 \ s} = \underline{8 \ m/s}$

b. i. Required:

The distance Bill will run for 3 seconds at the maximum speed;

Solution:

Distance, s = Speed, v × Time, t

The distance traveled at maximum speed in 3 seconds is therefore;

Distance = 8 m/s × 3 s = 24 m

The distance Bill travels in 3 seconds at the maximum speed is 24 meters.

ii) The distance Bill travels at 8 seconds after start, is given as follows;

Distance traveled in the first 5 seconds = 45 meters

Distance traveled in the next 3 seconds = 24 meters

Therefore;

• Bill's distance from the starting line 8 seconds after start is 45 meters + 25 meters = 69 meters

c. Bill's distance 6.5 seconds after the start of the race is given as follows;

Distance traveled in the first 5 seconds = 45 meters

Distance traveled in the next 1.5 seconds = 1.5 s × 8 m/s = 12 meters

• Bill's distance from the starting line 6.5 seconds after start of the race = 45 meters + 12 meters = 57 meters

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