Question

A body of mass 40kg is accelerating at a

rate of 9m/s²  . What is the rate of change of linear momentum?

Answer 1

Momentum = mass * velocity : p = mv
Time Rate of change of linear momentum of an object Δp / Δt
= Δ (m v ) / Δt = m Δv / Δt = m a
= Force acting on the object
= 40 Kg * 9 m /sec² = 360 Newtons
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Δ denotes change in a quantity. Δp = p2 - p1 Δt = t2 - t1
p2 = momentum at time t2 and p1 = momentum at time t1
v2 = velocity at time t2 v1 = velocity at time t1
a = acceleration, constant and same at t1 and t2
let u = velocity at time t = 0

Time rate of change of moment um is actually = (p2 - p1) / (t2 - t1)
p2 = m v2 p1 = m v1 So p2 - p1 = Δp = m (v2 - v1)

v2 = u + a t2 v1 = u + a t1 so, v2 - v1 = Δv = a (t2 - t1 ) = a Δt

So p2 - p1 = m (v2 - v1 ) = m a ( t2 - t1)
So ( p2 - p1 ) / (t2 - t1 ) = Δp / Δt = m a = 40 * 9 = 360 Newtons

Answer 2

Momentum = (mass) x (speed)

Mass is constant, so the rate of change of momentum is
(mass) x (rate of change of speed) .

But (rate of change of speed ) is just acceleration.

So the rate of change of momentum is (mass) x (acceleration).

But (mass) x (acceleration) is Force.

So Force is the rate of change of momentum. Verrrrrrrry interesting !

In this problem, Force = (40 kg) x (9 m/s²) = 360 newtons.

One 'Newton' is one kilogram-meter per second² .
Unit of momentum is (kilogram)-(meter per second), so 'newton'
is also a unit of time rate of change of momentum.

Rate of change of momentum is 360 momentum units per second.