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Kinetic energy Derivation of kinetic energy

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Page 1: Kinetic energy Derivation of kinetic energy. Kinetic Energy 2 starting equations F = m x a (Newton’s 2 nd law) W = Force x distance

Kinetic energy

Derivation of kinetic energy

Page 2: Kinetic energy Derivation of kinetic energy. Kinetic Energy 2 starting equations F = m x a (Newton’s 2 nd law) W = Force x distance

Kinetic Energy

2 starting equations F = m x a (Newton’s 2nd law) W = Force x distance

Page 3: Kinetic energy Derivation of kinetic energy. Kinetic Energy 2 starting equations F = m x a (Newton’s 2 nd law) W = Force x distance

Kinetic Energy

2 starting equations Force = m x a (Newton’s 2nd law) W = Force x distance Together give

Work = (m x a) x distance

W = m x a x d

Page 4: Kinetic energy Derivation of kinetic energy. Kinetic Energy 2 starting equations F = m x a (Newton’s 2 nd law) W = Force x distance

Work is MAD

Av Speed (velocity) is distance

time

Page 5: Kinetic energy Derivation of kinetic energy. Kinetic Energy 2 starting equations F = m x a (Newton’s 2 nd law) W = Force x distance

Work is MAD

Av Speed (velocity) is distance

time

Distance = Average velocity x time

Page 6: Kinetic energy Derivation of kinetic energy. Kinetic Energy 2 starting equations F = m x a (Newton’s 2 nd law) W = Force x distance

Work is MAD

Av Speed (velocity) is distance

time

Distance = Average velocity x time

Distance = v + u x t

2

Page 7: Kinetic energy Derivation of kinetic energy. Kinetic Energy 2 starting equations F = m x a (Newton’s 2 nd law) W = Force x distance

Distance

Distance = v + u x t

2

D = ½ x v + u x t

Starting velocity is zero

D = ½ x v x t

Page 8: Kinetic energy Derivation of kinetic energy. Kinetic Energy 2 starting equations F = m x a (Newton’s 2 nd law) W = Force x distance

Time

Final velocity = acceleration x time

Time = final velocity

acceleration

t = v

a

Page 9: Kinetic energy Derivation of kinetic energy. Kinetic Energy 2 starting equations F = m x a (Newton’s 2 nd law) W = Force x distance

Going back a step…..

D = ½ x v x t

D = ½ x v x v

a

D = ½ x v2

a

Page 10: Kinetic energy Derivation of kinetic energy. Kinetic Energy 2 starting equations F = m x a (Newton’s 2 nd law) W = Force x distance

Put into previous statements

W = m x a x d

W = m x a x ½ x v2

a

W = m x ½ x v2

W = ½ x m x v2