Question

With an average acceleration of-1.2 m/s^2 how much time will it take a cyclist to bring a bicycle with an initial velocity of 6.5m/s to a complete stop

Answer 1

Average acceleration
`\bar a` given initial and final velocities
`v_i` and
`v_f`, respectively, over a time interval lasting
`t` is

`\bar a=\frac{v_f-v_i}t`

from which we find

`t=(v_f-v_i)/(\bar a)`

To arrive at a complete stop, the cyclist's final velocity will be 0 m/s, so the time it takes to do so is

`t=(-6.5\,(\mathrm m)/(\mathrm s))/(-1.2\,(\mathrm m)/(\mathrm s^2))=5.4\,\mathrm s`