50
N·s
50
N·s
50
kg·m/s
25
m/s
50
m/s²
50
kg·m/s
50
N·s
50
N·s
50
kg·m/s
25
m/s
50
m/s²
50
kg·m/s
The Impulse Calculator computes the impulse delivered to an object when a force acts over a period of time. Impulse is one of the cornerstone concepts in mechanics, directly linking force and momentum change through the impulse-momentum theorem:
$$J = F \cdot \Delta t = \Delta p$$
Impulse has the same units as momentum (N·s or equivalently kg·m/s) and tells you how much an object's momentum changes during an interaction. A large impulse can come from a large force over a short time (a bat hitting a ball) or a small force over a long time (a tugboat pushing a ship).
This principle is the physics behind airbags and crumple zones: by extending the collision time, they reduce the peak force while delivering the same impulse needed to stop the occupant. Sports, automotive safety, ballistics, and rocketry all rely on impulse analysis. Enter the average force and time duration to get the impulse, and optionally provide mass to find the resulting velocity change.
The impulse-momentum theorem is derived directly from Newton's second law:
$$F = \frac{dp}{dt} \quad \Rightarrow \quad F \, dt = dp$$
Integrating over time: $$J = \int F \, dt$$
For a constant (average) force: $$J = F_{\text{avg}} \cdot \Delta t$$
Since $$J = \Delta p = m \Delta v$$, the velocity change is: $$\Delta v = \frac{J}{m} = \frac{F \cdot \Delta t}{m}$$
The calculator computes the impulse from force and time, then uses the optional mass to determine how much the velocity changes. This is exactly the same as computing the momentum change: $$\Delta p = J$$.
A positive impulse means force acts in the positive direction, increasing momentum in that direction. A negative impulse decelerates or reverses the object's motion. The magnitude tells you the total momentum transferred regardless of direction. If two scenarios deliver the same impulse magnitude, the velocity change depends only on the object's mass. Heavier objects experience smaller velocity changes for the same impulse — that is why trucks are harder to stop than bicycles.
Inputs
Results
A 100 N force over 0.5 s delivers 50 N·s of impulse, changing a 2 kg ball's velocity by 25 m/s.
Inputs
Results
An airbag exerting 5000 N over 0.08 s delivers 400 N·s, decelerating a 70 kg person by about 5.7 m/s (~20 km/h).
Impulse is the product of force and the time interval over which it acts: $$J = F \Delta t$$. It equals the change in momentum of the object. The SI unit is the newton-second (N·s), which is equivalent to kg·m/s.
The impulse-momentum theorem states that the impulse delivered to an object equals its change in momentum: $$J = \Delta p = m(v_f - v_i)$$. It is derived directly from Newton's second law and is one of the most useful relationships in mechanics for analyzing collisions and impacts.
In a crash, the occupant must lose all their momentum (fixed $$\Delta p$$). Since $$J = F \Delta t = \Delta p$$, increasing $$\Delta t$$ (the stopping time) reduces the average force $$F$$. Airbags extend the deceleration time from milliseconds to about 30-80 ms, dramatically reducing peak forces on the body.
Impulse is a vector quantity, pointing in the same direction as the applied force. In one dimension, the sign indicates direction: positive impulse increases momentum in the positive direction, negative impulse acts in the opposite direction.
Impulse ($$J = F \Delta t$$) changes an object's momentum and involves force and time. Work ($$W = F \Delta x$$) changes an object's kinetic energy and involves force and displacement. Both are force-based but describe different aspects of the interaction.
Yes. Negative impulse means the force (and therefore the momentum change) acts in the negative direction. For example, when you catch a ball, the impulse you apply is opposite to the ball's motion, bringing it to rest.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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