# Impulse Formula

A car is traveling at full speed. It crashes into the barrier, because of the negligence of the driver.

Here huge force is applied on the wall by the car in a very little time interval which we term as an impulse.

Impulse is the big force acting for a very small interval of time. It is represented by J⃗ J→.

Impulse Formula is articulated as

$J&space;=\,&space;F\times\,&space;t$

Where,
Force applied = F⃗,

Time interval throughout which force is applied = t.

Impulse can also be articulated as the rate of change of momentum.

$J&space;=\,&space;m\times\,&space;v$

Where,
Mass of the body = m and

Velocity with which body is moving = v.

Velocity is articulated as

$v&space;=\,&space;v_{f}\,&space;-\,&space;v_{i}$

Where,
Initial Velocity = vi and

Final Velocity = vf .
Therefore, the Impulsive force is articulated as

$f&space;=\,&space;m\frac{v_{f}-v_{i}}{t}$

Impulse is articulated in Kgms-1 and Impulsive force is articulated in Newton(N).

Solved Samples – Impulse

Below are some problems on impulse:

Problem 1: A batsman knocks back a ball straight in the direction towards the bowler without altering its initial speed of 12 m/s. If the mass of the ball is 0.15kg, calculate the impulse imparted to the ball?

Known:

vi (Initial Velocity) = 12 m/s,
vf (Final Velocity) = -12m/s,
m (mass) = 0.15kg,
J (Impulse) = ?
Impulse is articulated as
J = mvf – mv
= m(vf – vi)
= 0.15 Kg (-12 -12) m/s
= -3.6N.
Problem  2: A golfer hits a ball of mass 45g at a speed of 40m/s. The golf club is in contact with the ball for 3 s. Compute the average force applied by the club on the ball?

m (Mass)= 0.045 kg,
vi (Initial Velocity) = 0,
v(Final Velocity) = 40m/s,

$Impulse\,&space;Force\,&space;F\,&space;=\,&space;ma\,&space;=\,&space;m\,&space;\frac{v_{f}-v_{i}}{t}$

$=\,&space;0.045\,&space;\times\,\frac{40}{.003}$

$=\,&space;600N.$

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