A bicycle has wheels with a diameter of 0.630 m. It accelerates uniformly and the rate of rotation of its wheels increases from 225 rpm to 260 rpm in a time of 28.7 s. Find the linear acceleration of the bicycle.

the linear acceleration of the bicycle is 0.0403m/s²

Explanation:

First convert the angular given speeds to radians per second :  

ω₀ = 225rev/min×(2πrad/rev)×(1.00min/60.0sec)

= 23.56 rad/s

ω =  269rev/min×(2πrad/rev)×(1.00min/60.0sec)

= 27.23 rad/s

The angular acceleration is needed to find the tangential (linear) acceleration, it is :  

ω = ω₀ + αt

α = (ω - ω₀) / t

= (27.23rad/s - 23.56rad/s) / 28.7s

= 0.128rad/s²

The linear acceleration is :

linear acceleration = angular acceleration * r

a = rα

r = d/2

r = 0.630/2 = 0.315

a = rα

= (0.315m)(0.128rad/s²)

= 0.0403m/s²

Hence, the linear acceleration of the bicycle is 0.0403m/s²

whichever one it is, it's definitely not one that you included on the list you provided.

kepler used the data from tycho blahe (his mentor) to construct the laws of planetary motion.