1. Laws of Motion

1. Meaning: distance is the length of the actual path travelled by an object while going from one point to another, whereas displacement is the minimum (straight-line) distance between the starting point and the finishing point.
2. Type of quantity: distance has only magnitude, so it is a scalar; displacement has magnitude as well as direction, so it is a vector.
3. Dependence on path: distance depends on the path followed, whereas displacement depends only on the initial and final positions.
4. Zero value: distance travelled by a moving object is never zero, whereas displacement can be zero when the object returns to its starting point.
5. Comparison: distance is always greater than or equal to displacement; the two are equal only when the object moves along a straight line in one direction.
6. Example: when Swaralee walks once round a circular field of radius 100 m, the distance is 2πr = 2 × 3.14 × 100 = 628 m, but her displacement is zero.

1. Meaning: in uniform motion an object covers equal distances in equal intervals of time, whereas in non-uniform motion it covers unequal distances in equal intervals of time.
2. Speed: in uniform motion the speed remains constant; in non-uniform motion the speed keeps changing.
3. Acceleration: uniform motion along a straight line has zero acceleration, whereas non-uniform motion is accelerated motion.
4. Distance-time graph: for uniform motion the graph is a straight line; for non-uniform motion it is a curve or an irregular line.
5. Example: Amar’s car, which covers 20 km in every 30 minutes, is in uniform motion. A vehicle driven through heavy traffic, or Akbar’s car in the textbook table, is in non-uniform motion.

Table 1 — using v = u + at

Table 2 — using s = ut + ½at²

Table 3 — using v² = u² + 2as

Explanation: an object may follow a long, winding path, but displacement is measured only along the straight line joining the starting and finishing points, in a definite direction. If Prashant walks straight from home to school (1300 m) while Sheetal goes via Sangeeta’s house (500 m + 1200 m = 1700 m), both have the same displacement of 1300 m.

Explanation: when the velocity of an object decreases with time, the final velocity is less than the initial velocity, so a = (v − u)/t comes out negative. This negative acceleration is called deceleration, and its direction is opposite to the direction of velocity — for example, a car slowing down when the brakes are applied.

Explanation: in uniform circular motion the speed remains constant, but the object moves along the tangent at each point, so the direction of motion keeps changing. Since velocity depends on direction as well as speed, the velocity changes at every point. That is why uniform circular motion is accelerated motion.

Explanation: according to the law of conservation of momentum, when no external force acts on two colliding objects, the total momentum before the collision equals the total momentum after the collision. The momentum only gets redistributed — one object loses as much as the other gains.

Explanation: the rocket pushes hot gases out of its nozzle downward with great force (action). The gases push the rocket upward with an equal and opposite force (reaction), and this lifts the rocket. The same law explains why total momentum stays constant during the launch of a rocket.

• A freely falling object moves only under the gravitational force of the earth.
• Near the surface of the earth this force on a given object remains the same, so by F = ma the acceleration it produces also remains the same.
• Hence the velocity of the object increases by equal amounts in equal intervals of time — about 9.8 m/s in every second.
• Therefore the acceleration of a freely falling object is uniform. It is called the acceleration due to gravity, g = 9.8 m/s² (neglecting air resistance).

• Two equal and opposite forces cancel each other only when they act on the same object.
• Action and reaction forces always act on two different objects. When a gun fires a bullet, the action force acts on the bullet and the reaction force acts on the gun.
• Each force produces its own effect on the object it acts on — the bullet moves forward and the gun recoils backward.
• Therefore, even though they are equal and opposite, the effects of action and reaction forces do not get cancelled.

• Momentum is the product of mass and velocity (P = mv).
• A cricket ball has a much greater mass than a tennis ball, so at the same velocity it has much greater momentum.
• To stop a ball its momentum must be brought to zero, and the force needed depends on the rate of change of momentum.
• The tennis ball has less momentum, so a smaller force is enough to stop it in the same time. Hence it is easier to stop a tennis ball than a cricket ball.

• An object at rest does not change its position, so its displacement in every interval of time is zero.
• Its velocity is therefore zero at every instant, and it remains zero as long as the object stays at rest.
• Since the velocity does not change with time, the change in velocity is zero and the acceleration is also zero.
• A velocity that does not change with time is uniform. Therefore the velocity (zero) of an object at rest is considered to be uniform.

1. Passengers fall forward when a moving bus stops suddenly — First law (inertia of motion). The bus stops, but the upper part of the passenger’s body continues to move forward because of inertia, so the passenger leans forward.
2. Dust comes out when a carpet is beaten with a stick — First law (inertia of rest). The carpet suddenly moves forward, but the dust particles tend to remain at rest because of inertia, so they separate from the carpet and fall off.
3. A fielder pulls his hands backward while catching a fast cricket ball — Second law. Moving the hands back increases the time in which the ball’s momentum becomes zero. The rate of change of momentum decreases, so the force on the hands is smaller and they are not hurt. A thick sand bed for a high jumper works the same way.
4. An empty handcart is easier to push than a loaded one — Second law (F = ma). To give the same acceleration, the loaded cart with greater mass needs a greater force.
5. We are able to walk on the ground — Third law. While walking, our foot pushes the ground backward (action) and the ground pushes our foot forward with an equal and opposite force (reaction), which moves us ahead. Rowing a boat, swimming and a gun’s recoil are explained in the same way.

Answer: the average speed of the object is 6 m/s.

Answer: the applied force is 48 N and the acceleration of the 24 kg object is 2 m/s².

Answer: the bullet and the plank move together with a velocity of about 0.016 m/s.

Answer: the average speed of the swimmer is 2.25 m/s.

Some common devices you can start your project with:

For each device, collect a picture, describe how it works, and write which law of motion it is based on.