A wheel 80.0 cm in diameter accelerates uniformly from 215 rpm to 360 rpm. If in this process a point on the edge of this wheel have traveled 118 m, how long does this process take?

C = pi*D = 3.14 * 80 = 251.3cm = 2.51m

C=2.51m/rev=2.51m/6.28rad=2.51m/360Deg.

Rev = 118m * (1/ 2.51)rev/m = 47.

360 - 215 = 145rev/min.
t = 47rev * (1/145)min/rev = 0.324min.
= 19.4s.

To find the time it takes for the wheel to accelerate from 215 rpm to 360 rpm, we can use the formula for linear distance traveled by a point on the edge of a rotating object:

Distance = Circumference of the wheel * Number of revolutions

First, let's find the circumference of the wheel using its diameter:

Circumference = π * diameter

Given that the diameter is 80.0 cm, we can calculate the circumference:

Circumference = π * 80.0 cm

Next, we need to find the difference in the number of revolutions made by the wheel. As it accelerates uniformly, the increase in revolutions can be calculated as:

ΔRevolution = Final revolutions - Initial revolutions

ΔRevolution = 360 rpm - 215 rpm

Now we can calculate the linear distance traveled by the point on the edge of the wheel:

Distance = Circumference * ΔRevolution

Substituting the values in:

Distance = (π * 80.0 cm) * (360 rpm - 215 rpm)

Given that the distance is 118 m, we need to convert the units:

Distance = 118 m = 11800 cm

Now, we can solve for the time taken:

Time = Distance / (Circumference * ΔRevolution)

Substituting the values, we have:

Time = (11800 cm) / [(π * 80.0 cm) * (360 rpm - 215 rpm)]

Simplifying the equation and converting the units:

Time = (11800 cm) / [(π * 80.0 cm) * (145 rpm)]

Finally, we can calculate the time using the formula:

Time = (11800 cm) / (π * 80.0 cm * 145 rpm)

Calculating this expression will give us the time it takes for the process to occur.