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

Answer:

t=2s

Explanation:

The definition of power is:

$P=\frac{W}{t}$

And the work-energy theorem states that:

$W=\Delta K$

Since the movement starts from rest, we have that:

$\Delta K=\frac{mv_f^2}{2}-\frac{mv_0^2}{2}=\frac{mv_f^2}{2}$

And putting all together:

$P=\frac{mv_f^2}{2t}$

Since we want the time taken:

$t=\frac{mv_f^2}{2P}$

Which for our values is:

$t=\frac{(120kg)(5m/s)^2}{2(746W)}=2s$

Answer 2

Answer:

time = 2s

Explanation:

Power is:

$P=\frac{W}{t}$

work-energy theorem states that:

$W=\Delta K$

Since the movement starts from rest, we have that:

$\Delta K=\frac{mv_f^2}{2}-\frac{mv_0^2}{2}=\frac{mv_f^2}{2}$

And putting all together:

$P=\frac{mv_f^2}{2t}$

the time taken:

$t=\frac{mv_f^2}{2P}$

Which for our values is:

$t=\frac{(120kg)(5m/s)^2}{2(746W)}\\= 2s$