A cyclist rides a bicycle with a wheel radius of `0.500 m` across campus. A piece of plastic on the front rim makes a clicking sound every time it passes through the fork. If the cyclist counts `320` clicks between her apartment and the cafeteria, how far has she travelled ?

The front wheel on an ancient bicycle has radius 0.5 m. It moves with angular velocity given by the function omega(t) =2 +4t^2 , where t is in seconds. About how far does the bicycle move between t =2 and t =3 seconds ?

A bicycle is traveling downhill at a high speed. Suddenly, the cyclist sees that a bridge ahead has collapsed, so she has to stop. What is the maximum magnitude of acceleration the bicycle can have if it is not to flip over its front wheel—in particular, if its rear wheel is not to leave the ground? The slope makes an angle of 37^@ with the horizontal. On level ground, the centre of mass of the woman–bicycle system is at a point 1.0 m above the ground, 1.0 m horizontally behind the axle of the front wheel, and 35.0 cm in front of the rear axle. Assume that the tires do not skid.

A bicycle is traveling downhill at a high speed. Suddenly, the cyclist sees that a bridge ahead has collapsed, so she has to stop. What is the maximum magnitude of acceleration the bicycle can have if it is not to flip over its front wheel—in particular, if its rear wheel is not to leave the ground? The slope makes an angle of 37^@ with the horizontal. On level ground, the centre of mass of the woman–bicycle system is at a point 1.0 m above the ground, 1.0 m horizontally behind the axle of the front wheel, and 35.0 cm in front of the rear axle. Assume that the tires do not skid.