The core idea
Motion describes how position changes. Net force explains a change in velocity. Work and energy describe transfers that can produce motion, lift an object or warm its surroundings. These ideas are connected, but each answers a different question.
1. Motion depends on a reference point
Position tells us where an object is relative to a chosen reference. A bus passenger may remain at rest relative to the seat while moving relative to the road. Neither statement is a contradiction: they use different references. For a straight road, we can call the school gate zero and choose east as positive. A position of +40 m then means forty metres east of the gate; −10 m means ten metres west.
Distance is the total length of the path travelled. Displacement is the change from starting position to finishing position, including direction. Walk 60 m east and then 20 m west. Your distance is 60 + 20 = 80 m, but your displacement is +60 − 20 = +40 m. Returning to the gate would make total displacement zero even though you had certainly walked a distance.
2. Speed and velocity use different numerators
Average speed = total distance ÷ total elapsed time. If that 80 m walk took 40 seconds, average speed is 80 ÷ 40 = 2 m/s. Average velocity = displacement ÷ elapsed time, so it is 40 ÷ 40 = 1 m/s east. Include pauses in the elapsed time if you are describing the entire journey. An average does not mean you moved at that speed during every second.
Units prevent misleading answers. To convert 36 km/h into m/s, use 36 × 1,000 ÷ 3,600 = 10 m/s. A cyclist moving around a circular track may keep the same speed but continually change velocity because direction changes. “Constant speed” and “constant velocity” therefore are not interchangeable. Constant velocity requires an unchanged speed and direction.
3. A position–time graph tells a story
In the graph below, imagine walking along a straight path east. At 0 seconds you are at the start; after 5 seconds you are 10 m east. From 5 to 10 seconds you remain at that position. Then you reach 30 m at 15 seconds. The height of a point gives position, not speed. The slope—the change in position divided by the change in time—gives velocity for each straight segment.
The first segment has velocity 10 ÷ 5 = 2 m/s east. The horizontal segment has zero velocity. The final segment gives (30 − 10) ÷ (15 − 10) = 4 m/s east. The whole trip has average speed 30 ÷ 15 = 2 m/s, including the pause. These are invented teaching values. They show why the steepest segment describes the fastest part of this journey, while the highest point merely shows the farthest eastward position.
4. Acceleration is a change in velocity
For straight-line motion, average acceleration = (final velocity − initial velocity) ÷ time interval. A trolley speeds up from 1 m/s to 5 m/s in 2 seconds. Its average acceleration is (5 − 1) ÷ 2 = 2 m/s². Read the unit as a change of two metres per second in velocity for each second, if that acceleration stays constant. It does not mean the trolley travels two square metres.
If east is positive, an eastward-moving trolley that slows from +5 to +1 m/s has negative acceleration. The minus sign gives a direction relative to our chosen axis; it does not universally mean slowing down. A westward-moving object can speed up while having negative acceleration. This is why a diagram and stated direction are useful before substituting numbers into a formula.
5. Add the forces before predicting the motion
A force is an interaction that can change motion. Forces have size and direction. Suppose someone pushes a trolley east with 15 N while friction acts west with 5 N. The net horizontal force is 10 N east. In the simple constant-mass model, net force F = ma: m is mass in kilograms and a is acceleration in m/s². If the trolley’s mass is 5 kg, its acceleration is 10 ÷ 5 = 2 m/s² east. Use the net force, not the push alone.
A book resting on a table has downward gravitational force and upward support from the table. They balance, so its velocity does not change. Balanced forces can also act on a moving object: if driving force balances resistance on a straight road, a vehicle can move at constant velocity. Newton’s first law concerns zero net force, not the absence of every force.
Sources: NCERT Physics: Laws of Motion ↗
6. Action and reaction act on different objects
When you push a wall, the wall pushes back on you with an equal and opposite force. The forces do not cancel in the calculation for your body because one acts on the wall and the other on you. By contrast, the downward weight and upward table support both act on the book. Those can balance in the book’s force calculation. Distinguish “opposite forces” from a Newton’s-third-law pair.
Sources: NCERT Physics: Laws of Motion ↗
7. Work measures a particular energy transfer
For a constant force along the displacement, work = force × distance moved along that force. A 10 N force acting along a 3 m displacement does 30 J of work. A joule is a newton metre. A force opposite the displacement does negative work on that object; friction commonly does this to a sliding object. When force and displacement are not along the same line, only the force component along the displacement contributes.
Holding a bag still feels tiring, but the bag has no displacement, so your upward force does no mechanical work on the stationary bag during that interval. Your muscles still use chemical energy. Physics has not denied the effort: it has defined a specific measurable transfer. Power describes how quickly work is done: doing 60 J in 3 seconds gives an average power of 20 W.
Sources: NCERT Exploration: Work, Energy, and Simple Machines ↗
8. Account for energy before and after
At everyday speeds much lower than the speed of light, kinetic energy = ½mv², where m is mass and v is speed. A 2 kg object at 3 m/s has ½ × 2 × 3² = 9 J of kinetic energy. Doubling its speed to 6 m/s gives 36 J: four times as much, not twice. Near Earth’s surface, raising an object through height h increases gravitational potential energy by approximately mgh. Taking g = 10 m/s² as a rounded practice value, lifting a 2 kg bag by 1 m increases this energy by about 20 J.
When a trolley slows through friction, its kinetic energy becomes thermal energy in the surfaces and surroundings, with some sound. It has not disappeared. A useful energy account names the system and the transfers across its boundary. If you track only the trolley’s movement and ignore the floor and air, you will miss where part of the energy went. All numerical examples here are simplified teaching examples.
Sources: NCERT Exploration: Work, Energy, and Simple Machines ↗ · NCERT Physics: Laws of Motion ↗
PUT IT INTO PRACTICE
Solve a complete trolley problem
- A 4 kg trolley experiences a forward force of 14 N and a backward resistance of 6 N. Calculate net force and acceleration, stating direction.
- It starts from rest and maintains that acceleration for 3 seconds. Find its final speed. Then calculate its kinetic energy.
- Check your reasoning: net force = 8 N forward; acceleration = 2 m/s²; final speed = 6 m/s; kinetic energy = ½ × 4 × 36 = 72 J. Explain why using 14 N as net force would give the wrong answer.
Check your understanding
Can distance be positive while displacement is zero?
Yes. Walking out and returning to the same starting point gives a positive path length but no net change in position.
Does zero net force always mean an object is at rest?
No. In a reference frame that is not accelerating or rotating (an inertial frame), it means velocity does not change. The object may be at rest or move at constant velocity.
Why do action and reaction not cancel on a single object?
The two forces act on different objects. Only forces acting on the object being studied belong in its net-force sum.
A 3 kg object moves at 2 m/s. What is its kinetic energy?
½ × 3 × 2² = 6 J. Square the speed before multiplying; doubling speed would multiply kinetic energy by four at unchanged mass.