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(a) What is kinetic energy due to ? Deri...

(a) What is kinetic energy due to ? Derive an expression for it in case of a body of mass `m` moving with velocity `v`.
(b) If `W` is the work done to give a speed `v` to a car from rest, how much work is done to increase its speed to `2 v` ?

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### Step-by-Step Solution: #### (a) What is kinetic energy? Derive an expression for it in case of a body of mass `m` moving with velocity `v`. 1. **Definition of Kinetic Energy**: Kinetic energy (KE) is the energy possessed by an object due to its motion. The faster an object moves, the more kinetic energy it has. 2. **Work-Energy Principle**: According to the work-energy principle, the work done on an object is equal to the change in its kinetic energy. ...
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Knowledge Check

  • A constant force F is applied to a body of mass m moving with initial velocity u. If after the body undergoes a displacement S its velocity becomes v, then the total work done is

    A
    `m[v^(2)+u^(2)]`
    B
    `(m)/(2)[u^(2)+v^(2)]`
    C
    `(m)/(2)[v^(2)-u^(2)]`
    D
    `m[v^(2)-u^(2)]`

  • The kinetic energy passessed by a body of mass m moving with a velocity v is equal to (1)/(2)mv^(2) , provided

    A
    The body moves with velocities comparable to that of light.
    B
    The body moves with velocities negligible compared to the speed of light
    C
    The body moves with velocities greater than that of light
    D
    None of the above statement is correcst

  • The kinetic energy possessed by a body of mass m moving with a velocity v is equal to (1)/(2)mv^(2) , provided

    A
    The body moves with velocities comparable to that of light
    B
    The body moves with velocities negligible compared to the speed of light
    C
    The body moves with velocities greater than that of light
    D
    None of the above statement is correcst

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    A body of mass m moving with a velocity v strikes a statioinalry body of mass m and sticks to it. What is the speed of the system?

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