4. A rat named Littleguy runs in a treadmill (a wire wheel) with a diameter d =8.00 inches. In 5.00 minutes, Littleguy makes the treadmill rotate 2.80 x 10² times. If the rat were running along the ground, how far would he have run? What was his average velocity?
the circumference of the wheel is pi*d
revs * in/rev = in
2.8*10^2 * 8pi = 7037 in.
divide by the time to get the speed
To find out how far the rat would have run if he were running along the ground, we can use the circumference formula for a circle.
The formula to calculate the circumference of a circle is: C = πd, where C represents the circumference and d represents the diameter.
Given that the diameter of the treadmill is 8.00 inches, we can calculate the circumference:
C = π × d = π × 8.00 inches
The value of π is approximately 3.14, so we have:
C ≈ 3.14 × 8.00 inches
C ≈ 25.12 inches
So, the rat would have run approximately 25.12 inches if he were running along the ground.
To find the rat's average velocity, we need the formula for average velocity:
Average Velocity = Total Distance / Time
The rat's total distance is given by the circumference of the treadmill, which is approximately 25.12 inches. The total time is 5.00 minutes.
Average Velocity = 25.12 inches / 5.00 minutes
Average Velocity ≈ 5.02 inches/minute
Therefore, the rat's average velocity would be approximately 5.02 inches per minute.