Question

A driver increases his velocity from 20 km/hr to 100 km/hr. BY what factor does he increase the kinetic energy of the car with this increase in speed? Kinetic energy is 4 times greater
Kinetic energy is 16 times greater
Kinetic energy is 25 times greater
Kinetic energy is 9 times greater
Kinetic energy is 2 times greater

Answer 1

Answer:

25 times greater

Explanation:

Let the mass of the car is m

Initial speed, u = 20 km/h = 5.56 m/s

Final speed, v = 100 km/h = 27.78 m/s

The formula for the kinetic energy is given by

$K = \frac{1}{2}mv^{2}$

So, initial kinetic energy

$K_{i} = \frac{1}{2}m(5.56)^{2}$

Ki = 15.466 m

final kinetic energy

$K_{f} = \frac{1}{2}m(27.78)^{2}$

Kf = 385.86 m

Increase in kinetic energy is given by

= $\left ( \frac{K_{f}}{K_{i}} \right )$

= 385.86 / 15.466 = 25

So, the kinetic energy is 25 times greater.