Question

Which car has the most kinetic energy?

A. A car of mass 1000 kg with a speed of 3 m/s
B. A car of mass 2000 kg with speed 7 m/s
C. A car of mass 1000 kg with speed 7 m/s
D. A car of mass 2000 kg with speed 3 m/s

Answer 1

B. A car of mass 2000 kg with speed 7 m/s

Step-by-step explanation:

The kinetic energy of an object is given by:

`K=(1)/(2)mv^2`

where m is the mass of the object and v is its speed.

From the formula, we see that the larger the mass and the speed of the object, the larger its kinetic energy. Among the choices given, we see that the car with largest mass and largest speed is car B, which has a mass of 2000 kg and speed of 7 m/s. Its kinetic energy is:

`K=(1)/(2)(2000 kg)(7 m/s)^2=49,000 J`

We can verify that the other cars have smaller kinetic energy. In fact:

- Car A:
`K=(1)/(2)(1000 kg)(3 m/s)^2=4,500 J`

- Car C:
`K=(1)/(2)(1000 kg)(7 m/s)^2=24,500 J`

- Car D:
`K=(1)/(2)(2000 kg)(3 m/s)^2=9,000 J`

So, car B is the one which has most kinetic energy.