Here's a stationary bike. If you pedal such that the front wheel rotates at 6.9 rad/s, and that wheel's radius is half a meter, how far would you have gone in 35 minutes, if the bike where a non-stationary bike? (Assume a constant speed of rotation)

I am not sure where to start other than maybe using the formula s=or and converting the minutes to seconds. Would you have to use a linear equation?

r dθdt = .5 * 6.9 = 3.45 m/s is the linear speed.

so, 3.45 m/s * 35*60 s = 7245 m

To find the distance you would have gone on the non-stationary bike in 35 minutes, you can use the formula for linear distance, which is s = r × θ, where s is the distance travelled, r is the radius of the wheel, and θ is the angle of rotation.

First, you need to convert the time from minutes to seconds, since the formula requires time to be in seconds. There are 60 seconds in a minute, so 35 minutes would be 35 × 60 = 2100 seconds.

Next, you have the angular velocity (ω) of the front wheel, which is 6.9 rad/s. The angular velocity is the rate of change of the angle θ with respect to time t. In this case, the angle θ represents the total rotation of the wheel.

To find the angle of rotation (θ) in radians, you can multiply the angular velocity (ω) by the time (t) in seconds. So, θ = ω × t.

Now, substitute the values into the formula s = r × θ. The radius of the wheel is given as half a meter, so r = 0.5 meters.

s = (0.5 meters) × (6.9 rad/s) × (2100 seconds)

By performing the calculation, you will get the distance travelled in meters.