Question

a 1350-kg vehicle moves with a velocity of 19.0 m/s. calculate the power required to reduce the velocity to 4.90 m/s in 20.0 s.

Answer 1

A 1350-kg vehicle moves with a velocity of $19.0~\mathrm{m/s}$. Calculate the power required to reduce the velocity to $4.90~\mathrm{m/s}$ in 20.0 s. Please explain your answer.

Required power to reduce the velocity:

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

Work to slow down vehicle:

$$W = \Delta E _ {k} = \frac {m v _ {1} ^ {2}}{2} - \frac {m v _ {2} ^ {2}}{2} = \frac {m (v _ {1} ^ {2} - v _ {2} ^ {2})}{2}$$

Finally:

$$P = \frac {m (v _ {1} ^ {2} - v _ {2} ^ {2})}{2 t}$$ $$P = \frac {1350kg * ((19.0m/s) ^ {2} - (4.9m/s) ^ {2})}{2 * 20s} = 11373.4W$$

Answer: $P = 11373.4W$