IBPhysicsDPHLRevision NotesSpace, Time & MotionForces & MomentumCollisions & Explosions in One-Dimension

Collisions & Explosions in One-Dimension (DP IB Physics: HL): Revision Note

Written by: Ashika

Reviewed by: Caroline Carroll

Updated on 8 October 2026

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Collisions & Explosions in One-Dimension

Collisions are when two or more moving objects come together and exert a force on one another for a relatively short time
Explosions are when two or more objects that are initially at rest are propelled apart from one another
In both collisions and explosions, momentum is conserved, provided no external resultant force acts
- However, kinetic energy might not always be

Collisions in one dimension

Collisions in one dimension (1D) usually involve two objects interacting on a single straight line
- This means the velocity vectors before and after the collision are directed along the same axis and can be either positive or negative

A collision in one dimension between two objects A and B along the same line. Before the collision, object A moves towards stationary object B with velocity v0A. After the collision, A and B move away from each other with velocities vA, and vB respectively.

During a collision in one dimension between two objects, A and B, they move along the same line before and after the collision

Explosions in one dimension

Explosions in one dimension (1D) usually involve one stationary object becoming two objects that move away from each other along the same line
- Before the explosion, the velocity and, therefore, momentum, are zero
- After the collision, the velocity vectors are directed along the same axis and can be either positive or negative

An explosion in one dimension where a single object AB becomes two objects A and B moving along the same line in opposite directions. Before the explosion, object AB is at rest. After the explosion, A and B move away from each other with velocities vA, and vB respectively.

During an explosion in one dimension, a single object AB explodes and becomes two objects, A and B, which move along the same line in opposite directions

Elastic and inelastic collisions

Collisions can be either:
- elastic – if the kinetic energy is conserved
- inelastic – if the kinetic energy is not conserved
A perfectly elastic collision is an idealised situation that does not actually occur in everyday life
Perfectly elastic collisions do occur commonly between particles
- All collisions occurring on a macroscopic level are inelastic collisions
- However, exam questions can use the theoretical idea of an elastic collision on a macroscopic level

A totally inelastic collision is a special case of an inelastic collision where the colliding bodies stick together and move as one body
In a totally inelastic collision, the maximum amount of kinetic energy is transferred away from the moving bodies and is dissipated to the surroundings

Two balls move towards each other. After an elastic collision they move apart in opposite directions; after an inelastic collision they stick together and move off as one

In an elastic collision, kinetic energy is conserved. In a totally inelastic collision, the two objects stick together and move as one

An explosion is commonly associated with recoil
- For example, a gun recoiling after shooting a bullet or an unstable nucleus emitting an alpha particle and a daughter nucleus
- Kinetic energy is never conserved in an explosion, as the objects are always at rest initially
To find out whether a collision is elastic or inelastic, compare the kinetic energy before and after the collision
The equation for kinetic energy is:

$E_{k} = \frac{1}{2} m v^{2}$

Where:
- E_k = kinetic energy (J)
- m = mass (kg)
- v = velocity (m s^–1)

Examiner Tips and Tricks

It can be helpful to think about collisions and explosions as if there are four types rather than two:

elastic - kinetic energy conserved
perfectly elastic - kinetic energy conserved and no energy transferred between objects
inelastic - kinetic energy not conserved
totally inelastic - kinetic energy not conserved and maximum energy transferred to surroundings

Worked Example

Two similar spheres, each of mass m and velocity v are travelling towards each other. The spheres have a head-on elastic collision.

What is the total kinetic energy after the impact?

Two identical spheres move towards each other along a line, one with velocity v to the right and the other with velocity −v; the answer options are A ½mv², B 0, C mv² and D 2mv

Answer: C

In an elastic collision, kinetic energy is conserved, so:

kinetic energy before = kinetic energy after

kinetic energy before = ½mv² + ½mv² = mv²

Therefore, kinetic energy after = mv²

Worked Example

Trolley A of mass 0.80 kg collides head-on with stationary trolley B at speed 3.0 m s^–1. Trolley B has twice the mass of trolley A. The trolleys stick together and travel at a velocity of 1.0 m s^–1.

Determine whether this is an elastic or inelastic collision.

Answer:

Before the collision, trolley A moves right at 3.0 metres per second while B is stationary. After the collision, A and B stick together and move right at 1.0 metres per second.

Step 1: List the known quantities

Mass of trolley A, $m_{A} = 0.80 kg$
Initial velocity of trolley A, $u_{A} = 3.0 m s^{- 1}$
Mass of trolley B, $m_{B} = 2 m_{A} = 1.60 kg$
Initial velocity of trolley B, $u_{B} = 0$
Combined velocity of trolleys A and B, $v_{A + B} = 1.0 m s^{- 1}$

Step 2: Calculate the kinetic energy before the collision

$E_{k, b e f o r e} = \frac{1}{2} m_{A} {u_{A}}^{2} + \frac{1}{2} m_{B} {u_{B}}^{2}$

$E_{k, b e f o r e} = \frac{1}{2} \times 0.80 \times {(3.0)}^{2} + \frac{1}{2} \times 1.60 \times {(0)}^{2}$

$E_{k, b e f o r e} = 3.6 J$

Step 3: Calculate the kinetic energy after the collision

$E_{k, a f t e r} = \frac{1}{2} m_{A + B} {v_{A + B}}^{2}$

$E_{k, a f t e r} = \frac{1}{2} \times (0.80 + 1.60) \times {(1.0)}^{2}$

$E_{k, a f t e r} = 1.2 J$

Step 4: Determine the type of collision

Kinetic energy is not conserved in this collision
Therefore, this is an inelastic collision

Examiner Tips and Tricks

If an object is stationary or at rest, its initial velocity is 0, therefore, the momentum and kinetic energy are also equal to 0.

When a collision occurs in which two objects are stuck together, treat the final object as a single object with a mass equal to the sum of the masses of the two individual objects.

Kinetic energy depends on v², so it is never negative, whether the velocity is positive or negative.

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Collisions & Explosions in One-Dimension (DP IB Physics: HL): Revision Note

Collisions & Explosions in One-Dimension

Collisions in one dimension

Explosions in one dimension

Elastic and inelastic collisions

Examiner Tips and Tricks

Worked Example

Worked Example

Examiner Tips and Tricks

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Author: Ashika

Reviewer: Caroline Carroll