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?
A. sixteen times larger
B. the mass is needed
C. the same
D. Four times smaller
E. sixteen times smaller
F. four times larger
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.
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.