Motion, Force and Newton's Laws: Formulas and Facts
Physics notes on motion and force for exams: distance and displacement, velocity, acceleration, equations and graphs of motion, inertia, momentum and Newton's laws.
By GK24 Editorial Team· Published · 4 min read
Motion is the change in the position of a body with time, measured against something taken as fixed. A passenger seated in a moving train is at rest with respect to the train and in motion with respect to the platform, so every statement about motion carries a hidden reference point. This chapter supplies the vocabulary of mechanics and the three laws that explain why bodies move as they do, and examiners draw from it every year because the questions can be set either as definitions or as one line calculations.
Describing motion
Distance is the total length of the path covered and is a scalar, having magnitude only. Displacement is the shortest distance from the starting point to the finishing point, measured in a straight line, and is a vector, having both magnitude and direction. A runner who completes one lap of a circular track has covered a distance equal to the circumference but a displacement of zero. Displacement can be zero or negative; distance never is.
| Quantity | Definition | SI unit | Type |
|---|---|---|---|
| Distance | Length of the path covered | metre | Scalar |
| Displacement | Shortest distance between the initial and final positions | metre | Vector |
| Speed | Distance divided by time | metre per second | Scalar |
| Velocity | Displacement divided by time | metre per second | Vector |
| Acceleration | Change in velocity divided by time | metre per second squared | Vector |
Motion is uniform when equal distances are covered in equal intervals of time, however small the intervals; otherwise it is non-uniform. Acceleration is positive when the velocity increases and negative, called retardation, when it decreases. A body moving in a circle at constant speed is still accelerating, because its direction, and therefore its velocity, keeps changing.
The equations and graphs of motion
For a body moving with uniform acceleration, three equations connect the initial velocity u, the final velocity v, the acceleration a, the time t and the distance s.
- v equals u plus at
- s equals ut plus half of at squared
- v squared equals u squared plus twice as
Graphs say the same thing in pictures. On a distance-time graph the slope of the line gives the speed, so a straight line means uniform speed and a line parallel to the time axis means the body is at rest. On a velocity-time graph the slope gives the acceleration and the area under the graph gives the displacement. These two results are asked directly and are worth memorising as a pair.
Force and inertia
A force is a push or a pull that can change the state of rest or of motion of a body, change its direction, or change its shape. Its SI unit is the newton, and one newton is the force that gives a mass of one kilogram an acceleration of one metre per second squared. Forces acting on a body may be balanced, in which case the body's state does not change, or unbalanced, in which case it accelerates.
Inertia is the natural tendency of a body to resist a change in its state of rest or of uniform motion. It depends only on mass: the greater the mass, the greater the inertia, which is why a loaded truck is harder to start and harder to stop than a bicycle. Mass is therefore called the measure of inertia. The idea goes back to Galileo's experiments on inclined planes, which Newton turned into his first law.
Newton's three laws of motion
The first law states that a body continues in its state of rest or of uniform motion in a straight line unless an unbalanced external force acts on it. It is also called the law of inertia, and it explains why a passenger falls forward when a moving bus stops suddenly, the lower body stopping with the bus while the upper body keeps moving.
The second law states that the rate of change of momentum of a body is proportional to the applied force and takes place in the direction of the force. Momentum is the product of mass and velocity, written p equals mv, and its SI unit is the kilogram metre per second. From this law comes the familiar equation force equals mass times acceleration. It explains why a cricketer draws the hands back while catching a ball: lengthening the time of catching reduces the force needed to change the same momentum.
The third law states that to every action there is an equal and opposite reaction. The key point, and the one examiners test, is that the action and the reaction act on two different bodies, which is why they never cancel each other. A swimmer pushes the water back and is pushed forward, and a rocket pushes gases downward and is pushed upward.
Conservation of momentum
When no external force acts on a system, its total momentum stays the same. In the firing of a gun the bullet leaves with a large forward momentum and the gun moves back with an equal backward momentum, which is the recoil; because the gun is much heavier, its backward velocity is small. The same principle explains rocket propulsion and the behaviour of colliding bodies.
Exam Point of View
Questions come in three shapes. First, definitions and units: which quantity is a vector, the SI unit of force or of momentum, and what inertia depends on. Second, the laws themselves, usually as an example to be matched with a law: the passenger jerking forward is the first law, the cricketer drawing the hands back is the second, and the recoil of a gun or the swimmer pushing water is the third. Third, graph and formula questions, where the slope of a distance-time graph, the slope and area of a velocity-time graph, and the three equations of motion are asked directly or through a one step calculation. The commonest traps are treating distance and displacement as the same, forgetting that a body moving in a circle at constant speed is accelerating, and assuming that action and reaction cancel each other.
Important Facts
| SI unit of force | Newton; one newton equals one kilogram metre per second squared |
|---|---|
| SI unit of momentum | Kilogram metre per second |
| Scalar and vector | Distance and speed are scalars; displacement, velocity and acceleration are vectors |
| Equations of motion | v = u + at; s = ut + half at squared; v squared = u squared + 2as |
| Distance-time graph | Its slope gives the speed of the body |
| Velocity-time graph | Its slope gives acceleration and the area under it gives displacement |
| First law of motion | Law of inertia, foreshadowed by Galileo's work on inclined planes |
| Second law of motion | Force equals the rate of change of momentum, giving force equals mass times acceleration |
| Third law of motion | Action and reaction are equal and opposite and act on different bodies |
| Measure of inertia | The mass of the body |
| Conservation of momentum | Total momentum stays constant when no external force acts; explains recoil and rockets |
| Acceleration due to gravity | About 9.8 metre per second squared near the earth's surface |
Practice MCQs on this topic
Newton's first law of motion is also known by which name?
- A.Law of inertia
- B.Law of momentum
- C.Law of action and reaction
- D.Law of gravitation
Show answer
The first law states that a body continues in its state of rest or of uniform motion in a straight line unless an unbalanced external force acts on it, which is exactly the property called inertia.
Read the full explanation →Which of the following is a vector quantity?
- A.Distance
- B.Speed
- C.Displacement
- D.Time
Show answer
It is the shortest distance from the starting point to the finishing point together with the direction of that straight line, so it has both magnitude and direction and is therefore a vector.
Read the full explanation →The equation force equals mass multiplied by acceleration follows from which law of motion?
- A.First law
- B.Second law
- C.Third law
- D.Law of conservation of energy
Show answer
It states that the rate of change of momentum of a body is proportional to the applied force and takes place in the direction of the force.
Read the full explanation →The recoil of a gun when a bullet is fired is explained by the conservation of which quantity?
- A.Energy
- B.Linear momentum
- C.Mass
- D.Electric charge
Show answer
Before firing, the gun and the bullet are at rest, so the total momentum of the system is zero.
Read the full explanation →What is the SI unit of momentum?
- A.Newton
- B.Joule
- C.Kilogram metre per second
- D.Newton per second
Show answer
Momentum is the product of mass and velocity, so its unit is the unit of mass multiplied by the unit of velocity, that is kilogram multiplied by metre per second.
Read the full explanation →A passenger standing in a moving bus falls forward when the bus stops suddenly. This is due to
- A.Inertia of rest
- B.Inertia of motion
- C.Inertia of direction
- D.Centripetal force
Show answer
While the bus is moving, the passenger's whole body moves with it. When the brakes are applied, the feet stop along with the floor of the bus, but the upper body tends to keep moving forward at the same speed, and the passenger is thrown forward.
Read the full explanation →Which of the following is an equation of uniformly accelerated motion?
- A.v squared equals u squared plus 2as
- B.v equals u plus as
- C.s equals ut plus at
- D.v equals u plus at squared
Show answer
The three equations of uniformly accelerated motion are v equals u plus at, s equals ut plus half of a t squared, and v squared equals u squared plus twice a s, where u is the initial velocity, v the final velocity, a the acceleration, t the time and s…
Read the full explanation →The area under a velocity-time graph gives which quantity?
- A.Acceleration
- B.Displacement
- C.Force
- D.Momentum
Show answer
On a velocity-time graph the height of the curve is velocity and the base is time, so the area enclosed is velocity multiplied by time, which is displacement.
Read the full explanation →According to Newton's third law, action and reaction
- A.Act on the same body and cancel each other
- B.Act on two different bodies and do not cancel each other
- C.Are unequal in magnitude
- D.Act in the same direction
Show answer
The third law says that to every action there is an equal and opposite reaction, and the crucial point is that the two forces act on two different bodies.
Read the full explanation →The slope of a distance-time graph gives which quantity?
- A.Speed
- B.Acceleration
- C.Distance
- D.Momentum
Show answer
The slope of any graph is the change on the vertical axis divided by the change on the horizontal axis; here that is distance divided by time, which is speed by definition.
Read the full explanation →The inertia of a body depends on which of the following?
- A.Its velocity
- B.Its mass
- C.Its shape
- D.The force applied to it
Show answer
Inertia is the tendency of a body to resist any change in its state of rest or of uniform motion, and the heavier the body the harder it is to start or to stop.
Read the full explanation →A cricketer moves the hands backward while catching a fast ball because doing so
- A.Increases the momentum of the ball
- B.Increases the time of the catch and so reduces the force
- C.Reduces the mass of the ball
- D.Increases the acceleration of the ball
Show answer
Whether the hands are moved or not, the momentum of the ball must be brought down to zero.
Read the full explanation →Frequently Asked Questions
What is the difference between distance and displacement?
Distance is the total length of the path actually travelled and is a scalar, so it has magnitude alone and is never negative. Displacement is the straight line from the starting point to the finishing point and is a vector, so it has both magnitude and direction. A runner completing one lap of a circular track covers a distance equal to the circumference but has a displacement of zero, which is the standard example in examinations.
Why does a passenger fall forward when a moving bus stops suddenly?
Because of the inertia of motion, described by Newton's first law. While the bus moves, the whole body of the passenger moves with it. When the brakes are applied, the feet and the lower body stop along with the bus, but the upper body tends to continue moving forward at the same speed, and the passenger is thrown forward. The reverse happens when a stationary bus starts suddenly and the passenger falls backward.
Why do action and reaction not cancel each other?
Because they act on two different bodies. When a swimmer pushes the water backward, the reaction of the water pushes the swimmer forward; the action is on the water and the reaction on the swimmer. Forces can cancel only when they act on the same body. This is the detail examiners test most often in questions on the third law of motion.
Can a body be accelerating while moving at constant speed?
Yes. Acceleration is the rate of change of velocity, and velocity includes direction. A body moving along a circular path at a constant speed is changing its direction at every instant, so its velocity is changing and it is accelerating. The force that produces this acceleration acts towards the centre of the circle and is called the centripetal force.
Why does a cricketer draw the hands back while catching a ball?
The ball's momentum has to be reduced to zero in either case, but by pulling the hands back the fielder increases the time over which that change happens. By the second law of motion, the force needed is the change of momentum divided by the time taken, so a longer time means a smaller force on the hands. The same reasoning explains crash helmets, air bags and the use of a sand pit in the long jump.
Sources
- Science (Class IX), chapters on motion and force and laws of motion — NCERT
- Physics Part I (Class XI), chapters on motion in a straight line and laws of motion — NCERT
