## 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

Where,

- Force applied is given as F
- Time interval throughout which force is applied is given as t.

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

Where,

- Mass of the body is given as m
- Velocity with which body is moving is given as v.

Velocity is articulated as

Where,

- Initial Velocity is given as v
_{i} - Final Velocity is given as v
_{f}.

Therefore, the Impulsive force is articulated as

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

## Impulse-momentum formula

Impulse-momentum formula is obtained from impulse-momentum theorem which states that change in momentum of an object is equal to impulse applied on the object. The formula is given as follows:

Impulse-momentum formula | J=Δp |

When the mass is constant | FΔt=mΔv |

When the mass is varying | Fdt=mdv+vdm |

As the SI unit of impulse and momentum are equal, it is given as Ns=kg.m.s^{-1}

### Solved Samples

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?

**Answer: **Known:

v_{i} (Initial Velocity) = 12 m/s,

v_{f} (Final Velocity) = -12m/s,

m (mass) = 0.15kg,

J (Impulse) = ?

Impulse is articulated as

J = mv_{f} – mv_{i}

= m(v_{f} – v_{i})

= 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?

**Answer: **m (Mass)= 0.045 kg,

v_{i} (Initial Velocity) = 0,

v_{f} (Final Velocity) = 40m/s,

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