Suppose you are riding a stationary exercise bicycle, and the electronic meter indicates that the wheel is rotating at 8.6 rad/s. The wheel has a radius of 0.30 m. If you ride the bike for 2070 s, how far would you have gone if the bike could move?

2070s*8.6/(2 pi) = number of wheel revolutions.

Multiply that number by 2 pi R for the distance you would have travelled.

The answer will be (2070s)*(8.6 rad/s)*R

R is the wheel radius

Well, if I were riding a stationary exercise bicycle, I'd probably still be in the same place, wondering why I'm not getting anywhere! But let's use some math to find out how far you'd have gone if the bike could actually move.

The formula to calculate distance traveled is given by: distance = angular velocity × radius × time

Plugging in the given values, we have:
distance = 8.6 rad/s × 0.30 m × 2070 s

Solving this equation, we get:
distance = 5339.4 meters

So, if the bike could move, you would have gone approximately 5339.4 meters. Just think of all the places you could have visited in that distance! But hey, at least you got a good workout out of it, right?

To calculate the distance you would have gone if the bike could move, you can use the formula:

Distance = (angular velocity) * (radius) * (time)

Given:
Angular velocity (ω) = 8.6 rad/s
Radius (r) = 0.30 m
Time (t) = 2070 s

Substituting the given values into the formula, we have:

Distance = (8.6 rad/s) * (0.30 m) * (2070 s)

Calculating this, we get:

Distance = 5316.6 meters

Therefore, if the bike could move, you would have gone approximately 5316.6 meters.

To find the distance you would have gone if the bike could move, you can use the formula:

Distance = Angular velocity × Time × Radius

In this case, the angular velocity is given as 8.6 rad/s, the time is 2070 s, and the radius is 0.30m.

Plugging in these values into the formula:

Distance = 8.6 rad/s × 2070 s × 0.30 m

To calculate the answer, you can multiply 8.6 by 2070 and then multiply the result by 0.30:

Distance = 8.6 × 2070 × 0.30

Calculating this expression gives us the final answer.