What is Impulse?
Impulse is the effect of a large force acting on an object for a very short interval of time. When a car crashes into a barrier, or a bat strikes a cricket ball, the huge force applied over that brief moment is called impulse.
Impulse is a vector quantity, represented by J, and its SI unit is Newton-second (N·s), which is equivalent to kg·m/s.
Impulse Formula
Using force and time:
$$J = F \times t$$
Where:
- J = Impulse (N·s)
- F = Force applied (N)
- t = Time interval over which the force acts (s)
Using change in momentum:
$$J = m \times \Delta v = m(v_f – v_i)$$
Where:
- m = Mass of the object (kg)
- v_f = Final velocity (m/s)
- v_i = Initial velocity (m/s)
Impulse-Momentum Theorem
The impulse-momentum theorem states that the impulse applied to an object equals the change in its momentum:
$$J = \Delta p$$
| Condition | Formula |
|---|---|
| When mass is constant | F·Δt = m·Δv |
| When mass is varying | F·dt = m·dv + v·dm |
Impulse vs Momentum — Key Differences
These two concepts are closely linked, and students often mix them up:
| Point | Impulse | Momentum |
|---|---|---|
| Definition | Effect of force over a short time | Quantity of motion an object has |
| Formula | J = F × t | p = m × v |
| When it applies | During a collision or force interaction | At any instant, for any moving object |
| Relationship | Impulse = change in momentum | Momentum changes due to impulse |
| SI Unit | N·s (same numeric value as kg·m/s) | kg·m/s |
Why Impulse Matters (Real-World Example)
Car airbags are a direct application of the impulse concept. During a crash, a passenger’s momentum has to drop to zero either way — but the force felt depends on how long that change takes.
- Without an airbag, the passenger stops almost instantly (very small t) → very large force → serious injury
- With an airbag, the stopping time increases slightly (larger t) → the same impulse now happens with much less force → reduced injury
This is exactly why cushioned dashboards, helmets, and crumple zones in cars all work the same way — they increase the time of impact to reduce the force experienced.
Solved Examples
Example 1: A force of 50 N acts on a ball for 0.2 seconds. Find the impulse.
Given: F = 50 N, t = 0.2 s
J = F × t
J = 50 × 0.2
J = 10 N·s
Example 2: A ball of mass 0.5 kg moving at 10 m/s is struck and reverses direction at 15 m/s. Find the impulse applied.
Given: m = 0.5 kg, v_i = 10 m/s, v_f = -15 m/s (opposite direction)
J = m(v_f – v_i)
J = 0.5 × (-15 – 10)
J = 0.5 × (-25)
J = -12.5 N·s (negative sign shows the impulse acted opposite to the ball’s original direction)
Example 3: A car of mass 1000 kg travelling at 20 m/s comes to a complete stop in 0.5 seconds during a crash. Find the average force experienced.
Given: m = 1000 kg, v_i = 20 m/s, v_f = 0 m/s, t = 0.5 s
J = m(v_f – v_i) = 1000 × (0 – 20) = -20,000 N·s
F = J / t = -20,000 / 0.5
F = -40,000 N (i.e., 40,000 N acting opposite to motion — this shows why sudden stops in crashes generate such large forces)
Frequently Asked Questions
Q1. Is impulse the same as force?
No. Force is the push or pull acting on an object at any moment. Impulse is the combined effect of that force acting over a specific time interval — it depends on both the force and how long it acts.
Q2. Can impulse be negative?
Yes. Since impulse is a vector, a negative value simply means the impulse acted in the opposite direction to the object’s original motion — it doesn’t mean “less” impulse.
Q3. What is the SI unit of impulse?
Newton-second (N·s), which is numerically equal to kg·m/s (the unit of momentum) — this is a direct consequence of the impulse-momentum theorem.
Q4. Why do airbags and helmets use the concept of impulse?
Because for the same change in momentum, increasing the time of impact reduces the force felt by the body. This is the core safety principle behind airbags, helmets, and cushioned surfaces.