A wheel 31 cm in diameter accelerates uniformly from 250 rpm to 370 rpm in 7.0 s. How far will a point on the edge of the wheel have traveled in this time?

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Answer 1

A wheel 31 cm in diameter accelerates uniformly from 250 rpm to 370 rpm in 7.0 s. A point on the edge of the wheel will have traveled approximately 196.218 cm in 7.0 seconds.

To calculate the distance traveled by a point on the edge of the wheel, we need to find the circumference of the wheel and then multiply it by the number of revolutions it completes in the given time.

The diameter of the wheel is given as 31 cm, which means the radius (r) of the wheel is half of the diameter:

r = 31 cm / 2 = 15.5 cm.

The circumference of the wheel can be calculated using the formula

C = 2πr.

Plugging in the radius value, we have:

C = 2π(15.5 cm).

Now, let's calculate the initial and final distances traveled by a point on the edge of the wheel.

Initial distance: The initial speed of the wheel is given as 250 revolutions per minute (rpm). To convert it to revolutions per second, we divide by 60:

250 rpm / 60 s = 4.17 revolutions per second.

Therefore, the initial distance traveled is:

Initial distance = 4.17 revolutions * C.

Final distance: The final speed of the wheel is given as 370 rpm. Converting it to revolutions per second:

370 rpm / 60 s = 6.17 revolutions per second.

Hence, the final distance traveled is:

Final distance = 6.17 revolutions * C.

To find the total distance traveled, we subtract the initial distance from the final distance:

Total distance = final distance - initial distance.

Now, let's calculate the values:

C = 2π(15.5 cm) = 97.4 cm (approx.)

Initial distance = 4.17 revolutions * 97.4 cm = 405.58 cm (approx.)

Final distance = 6.17 revolutions * 97.4 cm = 601.798 cm (approx.)

Total distance = 601.798 cm - 405.58 cm ≈ 196.218 cm.

Therefore, a point on the edge of the wheel will have traveled approximately 196.218 cm in 7.0 seconds.

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