Physics - Kinematics Question with Solution | TestHub

A bicycle rider is traveling at a constant speed along a straight road and then gradually applies the brakes during a time interval $0<t<t_f$ until the bicycle comes to a stop. The combined mass of the cyclist and bicycle is $m$. Assume that the magnitude of the braking acceleration increases linearly in time according to $f|a|=bt/m$, $0<t<t_f$, where $b>0$ is a constant. At the instant the person applies the brakes, a horizontal distance from the rider, the wind blows and snaps an iPod off the branch of the tree with a zero initial speed. The iPod was initially at a height $h$ above the ground. The cyclist catches the iPod at the instant the cyclist has come to a stop. You may assume that the cyclist catches it at a height $s$ above the ground.