Impulse Formula

The Formula

J = F\Delta t = \Delta p (change in momentum)

When to use: A big push for a short time or a small push for a long time can have the same effect.

Quick Example

Catching a ball: if you 'give' with it (more time), the force is less.

Notation

\vec{J} is impulse in N·s (or equivalently kg·m/s), \vec{F} is force in newtons, \Delta t is the time interval in seconds, and \Delta\vec{p} is the change in momentum.

What This Formula Means

The product of force and time interval, equal to the resulting change in an object's momentum.

A big push for a short time or a small push for a long time can have the same effect.

Formal View

Impulse is defined as \vec{J} = \int_{t_1}^{t_2} \vec{F}\, dt = \Delta\vec{p} = m\vec{v}_f - m\vec{v}_i. For a constant force, this simplifies to \vec{J} = \vec{F}\Delta t.

Worked Examples

Example 1

easy
A force of 200 \text{ N} acts on a ball for 0.05 \text{ s}. What is the impulse delivered to the ball?

Solution

  1. 1
    Recall the impulse formula: J = F \Delta t, where F is the applied force and \Delta t is the time interval.
  2. 2
    Identify the given values: F = 200 \text{ N}, \Delta t = 0.05 \text{ s}.
  3. 3
    Substitute and calculate: J = 200 \times 0.05 = 10 \text{ N s}

Answer

J = 10 \text{ N s}
Impulse is the product of force and the time interval over which it acts. It equals the change in momentum of the object.

Example 2

medium
A 0.15 \text{ kg} baseball moving at 40 \text{ m/s} is hit by a bat and reverses direction at 50 \text{ m/s}. What impulse did the bat deliver?

Common Mistakes

  • Using the total time instead of the time interval during which the force is actually applied — impulse only accumulates while the force acts.
  • Forgetting the vector nature of impulse — a force applied in the negative direction produces a negative impulse that reduces momentum.
  • Confusing impulse with work — impulse changes momentum (J = \Delta p), while work changes kinetic energy (W = \Delta KE).

Why This Formula Matters

Impulse explains why airbags and crumple zones save lives — by increasing the collision time, the peak force on passengers is dramatically reduced. It is fundamental to sports, vehicle safety, and ballistics.

Frequently Asked Questions

What is the Impulse formula?

The product of force and time interval, equal to the resulting change in an object's momentum.

How do you use the Impulse formula?

A big push for a short time or a small push for a long time can have the same effect.

What do the symbols mean in the Impulse formula?

\vec{J} is impulse in N·s (or equivalently kg·m/s), \vec{F} is force in newtons, \Delta t is the time interval in seconds, and \Delta\vec{p} is the change in momentum.

Why is the Impulse formula important in Physics?

Impulse explains why airbags and crumple zones save lives — by increasing the collision time, the peak force on passengers is dramatically reduced. It is fundamental to sports, vehicle safety, and ballistics.

What do students get wrong about Impulse?

Impulse equals the area under a force-time graph, not just force times a single moment.

What should I learn before the Impulse formula?

Before studying the Impulse formula, you should understand: momentum, force.

← Back to Impulse See All Examples Practice Problems