# A moving car has kinetic energy. If it speeds up until it is going four times faster than before, how many kinetic energy does it have in comparison?multiple choice: A. sixteen times larger B. the...

A moving car has kinetic energy. If it speeds up until it is going four times faster than before, how many kinetic energy does it have in comparison?

multiple choice:

A. sixteen times larger

B. the mass is needed

C. the same

D. Four times smaller

E. sixteen times smaller

F. four times larger

krishna-agrawala | Student

Kinetic energy of any object is given by the formula:

kinetic energy = k = (m*v^2)/2

Where: m = mass and v = speed of the object.

If speed of car v become four time than the increased kinetic energy

= [m*(4v)^2]/2 = (m*16*v^2)/2

Since the mass of the car (m) remains same, the ratio of increased energy at 4 times he speed to original speed:

=[(m*16*v^2)/2]/[(m*v^2)/2] = 16

Thus kinetic energy will increase 16 times in comparison.

Thus alternative A) is right.

neela | Student

The moving car with mass m, and velocity v ha the kinetic enegy, k1 =  (1/2)mv^2.............(1)

Now with 4 times the velocity it has a kinetic energy k2 = (1/2)m*(4v)^2 =8mv^2..............(2)

Therefore,the enrgy has increased by k2/k1 times = 8mv^2/[(1/2)mv^2] = 16 times.