Question

A car weighing $1ton$ is moving twice as fast as another car weighing $2ton$. The kinetic energy of the one-ton car is
A. less than that of the two-ton car is
B. same as that of the two-ton car is
C. more than that of the two-ton car is
D. impossible to compare with that of the two-ton car unless the height of each

Answer 1

Hint: Kinetic energy of an object is the energy it possesses due to its motion. To solve the given question, we will first equate the individual kinetic energy of each car, then compare both of them to find the required answer.

Formula used:
$K = \dfrac{1}{2}m{v^2}$

Complete step-by-step answer:
As we know that, kinetic energy is the energy an object has because of its motion. After the work is done, energy gets transferred to the object, and the object moves with a new constant speed. The transferred energy is known as kinetic energy, and it depends on the mass and speed achieved.
Kinetic energy possessed by the car weighing $1ton$ will be,
${K_1} = \dfrac{1}{2}{m_1}{v_1}^2$
Let the velocity of car weighing $2ton$ be, ${v_2} = v$
So, according to the question, a car weighing $1ton$ is moving twice as fast as another car weighing $2ton$. Thus, ${v_1} = 2v$
$ \Rightarrow {K_1} = \dfrac{1}{2}(1){(2v)^2} = 2{v^2}$
Now, Kinetic energy possessed by car weighing $2ton$ will be,
${K_2} = \dfrac{1}{2}{m_2}{v_2}^2$
$ \Rightarrow {K_2} = \dfrac{1}{2}(2){(v)^2} = {v^2}$
Now, comparing both of them, we conclude that since kinetic energy depends on the velocity of the object squared. This means that when the velocity of the object doubles, its kinetic energy quadruples. Therefore, the kinetic energy of the one-ton car is more than that of the two-ton car.

So, the correct answer is “Option C”.

Note: Some points one should remember while solving questions related to kinetic energy:
Kinetic energy of an object must always be either zero or a positive value, whereas velocity can be a positive or negative value, because velocity squared is always positive.
Kinetic energy is not a vector quantity. So, a ball thrown in the direction with a velocity $v$, has the exact same kinetic energy as with a ball thrown down with a velocity $v$.