A bug is moving back and forth on a straight path. The velocity of the bug is given by vt=t2-3t. Find the average acceleration o
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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
<h3>Methods used to calculate speed and distance traveled</h3>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, <em>t</em> = 10 s - 5 s = 5 s
Therefore;
b. i. Required:
The distance Bill will run for 3 seconds at the maximum speed;
Solution:
Distance,<em> s</em> = Speed, <em>v</em> × Time, <em>t</em>
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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 = <u>69 meters</u>
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 = <u>57 meters</u>
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