A runner covers one lap of a circular track 40.0 in diameter in 63.3 .
For that lap, what was her average velocity?
If she covered the first half-lap in 28.6 , what were her average velocity for that half-lap?
Her avg velocity is zero because her total displacement is zero around any closed path. This is because velocity is a vector quantity that depends on direction. Her average speed is non-zero, depending only on the distance she ran divided by the time. (Distance is a scalar quantity so direction doesn't matter.)
To find the average velocity, we can use the formula: average velocity = total distance / total time.
For the full lap:
The circumference of a circle is calculated using the formula C = π × d, where d is the diameter. So, the distance covered by the runner for one lap is:
distance = π × 40.0 = 125.6 meters
The total time taken by the runner to complete one lap is given as 63.3 seconds.
Therefore, the average velocity for the full lap is:
average velocity = distance / time = 125.6 / 63.3 = 1.99 meters per second (rounded to two decimal places).
For the first half-lap:
The distance covered by the runner for the first half-lap is half of the full lap distance:
distance = 125.6 / 2 = 62.8 meters
The total time taken by the runner to complete the first half-lap is given as 28.6 seconds.
Therefore, the average velocity for the first half-lap is:
average velocity = distance / time = 62.8 / 28.6 = 2.19 meters per second (rounded to two decimal places).
To find the average velocity, we need to divide the total distance covered by the total time taken.
For the first question, the runner covered one lap of a circular track with a diameter of 40.0 meters in 63.3 seconds. Since the circumference of a circle is given by πd (where d is the diameter), the distance covered by the runner is π(40.0) meters. Therefore, the average velocity is:
Average Velocity = Total Distance / Total Time
= π(40.0) meters / 63.3 seconds
To calculate this value, you need to know the value of π, which is approximately equal to 3.14159. Multiplying this value by 40.0 and then dividing by 63.3 will give you the average velocity in meters per second.
For the second question, the runner covered half a lap of the circular track (i.e., the first half-lap) in 28.6 seconds. Since it is only half a lap, the distance covered will be half the circumference of the circular track. Therefore, the distance covered by the runner is (1/2)π(40.0) meters. To find the average velocity, you divide this distance by the time taken:
Average Velocity = Total Distance / Total Time
= (1/2)π(40.0) meters / 28.6 seconds
Again, you can calculate this value by multiplying the appropriate values and then dividing the result by 28.6.