GeoRock > Computation > Calculation of Initial Velocity using the Impulse Theorem

The impulse theorem states that the impulse exerted on an object is equal to the change in the object's momentum. In formula, we can write it as:

I = Δp

Where:

•I is the impulse.

•Δp is the change in momentum.

Momentum p is defined as the product of mass m and velocity v:

p = m * v

If we know the force Fapplied to the mass and the time t during which this force is applied, the impulse I can be calculated as:

I = F * t

To find the initial velocity v0, we can express the change in momentum as:

Δp = m * v - m * v0

Where:

•v is the final velocity.

•v0 is the initial velocity.

Using the impulse theorem:

F * t = m * v - m * v0

From which we can isolate the initial velocity v0:

v0 = v - (F * t) / m

Example Calculation:

Suppose we have a mass with the following characteristics:

•Mass m = 10 kg

•A constant force F = 50 N is applied for t = 4 s

•Final velocity v = 30 m/s

Let's calculate the initial velocity v0:

1.Calculate the impulse:

I = F * t = 50 N * 4 s = 200 Ns

2.Using the formula to find v0:

v0 = v - (I / m)
v0 = 30 m/s - (200 Ns / 10 kg)
v0 = 30 m/s - 20 m/s
v0 = 10 m/s

Therefore, the initial velocity of the mass was 10 m/s.