Everything you need to know about Kinetic Energy.

Kinetic energy is a type of mechanical energy. It is the energy possessed by a body by virtue of its motion.

Examples of kinetic energy are:
1. A student running a race.
2. An object falling freely under gravity.
3. Wind or air in motion.
4. Electrical charges in motion.
5. A moving bullet or a moving hammer head.

Measurement of Kinetic Energy

Kinetic energy depends only on the mass and velocity of the body. The kinetic energy(K.E) of a body in motion is given by:
K.E=(1×mv²)/2
where
m is the mass of the object.(kg)
v is the velocity of the object(m/s).
K.E is the Kinetic energy(Joules).
    Thus if two bodies in motion have the same mass, the faster body has a greater kinetic energy and if they have the same velocity, the body with greater mass has a greater kinetic energy.

Derivation of the Kinetic Energy Formula. 

Workdone= Force ×Distance.
Force= mass × acceleration
Lets represent
W as workdone
a as acceleration
m as mass
v as velocity
g as acceleration due to gravity.
W= (ma) s=mas
according to newton equation of motion
v²=u²+2gs., u=0
v²=0+2gs, v²=2gs
gs=v²/2, g=a
as=v²/2
W=mas=m×v²/2= mv²/2.
K.E=W=mv²/2.

Solved Examples. 

1. An object of mass 5kg is moving at a constant velocity of 15m/s. calculate its kinetic energy.
   Solution.
Given,
mass=5kg
velocity =15m/s
K.E=mv²/2 = 5×15²/2=5×225/2
K.E=562.5joules

2. An object has a kinetic energy of 81joules and a mass of 2kg. Calculate its velocity.
  Solution.
Given,
mass=2kg
K.E=81joules
v=? K.E=mv²/2
81=2×v²/2(the two will cancel out)
81=v², to find v we need to take the square root of both sides.
√81= √v²
v=9m/s.

3. if the velocity of an object is 4m/s and its K.E is 64joules,find its mass.
Solution.
Given,
velocity =4m/s
K.E=64 joules
m=?
K.E =mv²/2
64=m×4²/2
64=m×16/2,cross multiply
64×2=m×16
128=16m. divide both sides by 16.
128/16=16m/16, m=8kg.

You can try these out.
1. A body has a mass of 3kg and velocity of 5m/s find its K.E.
2. A body moves at 6m/s at 60joules find its mass.
3. An object has a mass of 8kg and K.E of 12,find its velocity.

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