Question

Define KE and Derive it's formula for 3 marks.

Answer 1

Answer:

Definition:

• The energy possessed by a body by virtue of its motion is called kinetic energy.
• It is given as: K.E = 1/2 mv^2
• Its S.I unit is Joules.
• Its dimensional formula = ML^2T^-2

Derivation of the formula:

Consider a body of mass 'm' initially at rest. Let a force F be applied on the body which produces a small displacement ds in the same direction as the force. Then, work done = F•ds

dw = Fds × CosØ

( where Ø= angle between force and displacement. Here, Ø = 0 )

dw = Fds × Cos0 = Fds (since cos0 = 1)

Now, using second law of Newton,

F = dP/dt

F = d(mv)/dt = ma

then,

dw = (ma)ds = m(dv/dt) × ds (since a = dv/dt)

dw = mdv × ds/dt = mdv × v = mvdv

Integrating both sides,

W = m[(V^2)/2] (limits: from u to v)

W = m(v^2)/2 - (u^2)/2

Since, body was initially at rest, u = 0

W = (mv^2)/2 = 1/2 mv^2

Since, Energy = work done

hence, K.E = 1/2 mv^2