Impulse Formula
Reference for the impulse formula J = F*Δt, which calculates the change in momentum.
Covers impulse-momentum theorem, collision analysis, and force-time graphs.
The Formula
Impulse is the product of force and the time interval over which it acts. It equals the change in momentum of the object.
Variables
| Symbol | Meaning |
|---|---|
| J | Impulse (measured in Newton-seconds, N·s, or kg·m/s) |
| F | Average force applied (measured in Newtons, N) |
| Δt | Time interval during which the force acts (measured in seconds, s) |
| Δp | Change in momentum (measured in kg·m/s) |
| m | Mass of the object (measured in kilograms, kg) |
| Δv | Change in velocity (measured in meters per second, m/s) |
Example 1
A baseball (0.145 kg) is hit by a bat. It goes from -40 m/s (pitched) to +50 m/s (hit). What impulse was applied?
Calculate change in velocity: Δv = 50 - (-40) = 90 m/s
Apply the formula: J = mΔv = 0.145 × 90
J = 13.05 N·s
Example 2
If the bat contact lasted 0.001 seconds, what was the average force on the ball?
Rearrange: F = J / Δt = 13.05 / 0.001
F = 13,050 N (about 2,934 lbs of force — enormous but brief)
Example 3
A car airbag extends the collision time from 0.01s to 0.15s. If the impulse is 9,000 N·s, compare the forces.
Without airbag: F = 9,000 / 0.01 = 900,000 N
With airbag: F = 9,000 / 0.15 = 60,000 N
The airbag reduces the force by 15 times — from 900,000 N to 60,000 N
When to Use It
Use the impulse formula for problems involving forces that act over short time periods.
- Analyzing collisions between objects (cars, balls, particles)
- Understanding how safety devices work (airbags, crumple zones, helmets, padding)
- Calculating the force of impact during sports (bat hitting ball, foot kicking ball)
- Rocket propulsion — the impulse from exhaust determines thrust
- Any situation where you need to relate force, time, and change in motion