A runner covers one lap of a circular track 40.0 m in diameter in 62.5s (a) for that lap what were her average speed and average velocity? (b) if she covered the first half lap in 28.7 s, what were her average speed and average velocity for that half lap?
The final - initial positions in part b are on opposite sides of the circle. For distance run, you went half way around the track. (pi D/2)
For distance between beginning point and end point you do not go around the track, you draw a vector straight across from start to finish, thus just the diameter.(D)
In part a, your average velocity was ZERO, because your final position is the same as your initial position and you went nowhere. Of course your speed was pi D/62.5
speed=distanceran/time
velocity=(final position-initialposition)/time
I assume you know the distance around a circle (PI*diameter).
To find the average speed and average velocity, we need to understand the definitions of these terms:
Average Speed: The total distance covered divided by the total time taken.
Average Velocity: The displacement (change in position) divided by the total time taken.
(a) For the entire lap:
1. Calculate the distance covered by the runner: The distance is equal to the circumference of the circular track. The formula for circumference is given by C = πd, where d is the diameter. Therefore, the distance covered is C = π(40.0 m).
Distance = 3.14 x 40.0 m = 125.6 m
2. Use the formula for average speed: Average Speed = Distance / Time
Average Speed = 125.6 m / 62.5 s = 2.01 m/s
3. Since the runner completes a full lap, her displacement is zero (she ends up at the same position as she started). Therefore, her average velocity is also zero.
Average Velocity = 0 m/s
(b) For the first half lap:
1. Calculate the distance covered by the runner: For the first half lap, the runner covers half the circumference of the circular track. The distance covered is C/2, where C is the circumference.
Distance = (π x 40.0 m) / 2 = 62.8 m
2. Use the formula for average speed: Average Speed = Distance / Time
Average Speed = 62.8 m / 28.7 s = 2.18 m/s
3. Since the runner completes only half a lap, her displacement is half the circumference of the track (as she ends up at a different position from where she started). Therefore, her average velocity is non-zero, and its magnitude is equal to her average speed.
Average Velocity = 2.18 m/s (same as the average speed)
So, to summarize:
(a) For the entire lap: Average Speed = 2.01 m/s, Average Velocity = 0 m/s
(b) For the first half lap: Average Speed = 2.18 m/s, Average Velocity = 2.18 m/s