Question

A student connects a 1 hp motor to a bicycle. How much time will it take for the bicycle to accelerate from rest to a speed of 5.0 m/s if the combined mass of the student and the bicycle is 120 kg? (1 hp = 746 W)

Answer 1

time = 2s

Step-by-step explanation:

Power is:

`P=(W)/(t)`

work-energy theorem states that:

`W=\Delta K`

Since the movement starts from rest, we have that:

`\Delta K=(mv_f^2)/(2)-(mv_0^2)/(2)=(mv_f^2)/(2)`

And putting all together:

`P=(mv_f^2)/(2t)`

the time taken:

`t=(mv_f^2)/(2P)`

Which for our values is:

`t=((120kg)(5m/s)^2)/(2(746W))\\= 2s`

Answer 2

t=2s

Step-by-step explanation:

The definition of power is:

`P=(W)/(t)`

And the work-energy theorem states that:

`W=\Delta K`

Since the movement starts from rest, we have that:

`\Delta K=(mv_f^2)/(2)-(mv_0^2)/(2)=(mv_f^2)/(2)`

And putting all together:

`P=(mv_f^2)/(2t)`

Since we want the time taken:

`t=(mv_f^2)/(2P)`

Which for our values is:

`t=((120kg)(5m/s)^2)/(2(746W))=2s`