A boy walks 40 m North, then 30 m West, and finally 90 m South. If this entire motion takes2.50 minutes, determine his: a) average speed b) average velocity (mag and dir)
Question
A boy walks 40 m North, then 30 m West, and finally 90 m South. If this entire motion takes2.50 minutes, determine his: a) average speed b) average velocity (mag and dir)
Solution
a) Average Speed:
The average speed is calculated as the total distance traveled divided by the total time taken.
The total distance traveled by the boy is 40 m (North) + 30 m (West) + 90 m (South) = 160 m.
The total time taken is 2.50 minutes, which is equal to 2.50 * 60 = 150 seconds (since 1 minute = 60 seconds).
So, the average speed = total distance / total time = 160 m / 150 s = 1.07 m/s.
b) Average Velocity:
The average velocity is calculated as the total displacement divided by the total time taken.
The total displacement is the shortest distance from the initial to the final position.
The boy ends up 50 m South from his starting point (90 m South - 40 m North) and 30 m West.
We can use the Pythagorean theorem to calculate this displacement: sqrt((50 m)^2 + (30 m)^2) = 58.31 m.
The direction of the displacement is South-West.
So, the average velocity = total displacement / total time = 58.31 m / 150 s = 0.39 m/s, South-West.
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