Motion

When an object changes its position relative to its surroundings over time, it is said to be in motion. This phenomenon of a change in position is referred to as motion.

Motion is the change of an object's position relative to its surroundings over time.

Rest is the opposite of motion. When an object does not change its position relative to its surroundings over time, it is said to be in rest.

Deduct F=ma from Newton's second law of motion.

Let us assume that an object of mass m moving with an initial velocity u. Then a force of magnitude F is applied to it for a duration of time t which changes the velocity of the object to v.
∴ initial momentum of the object = mu
   final momentum of the object = mv
The change in momentum after t time = $\mathrm{mv}-\mathrm{mu}$
The rate of change in momentum = $\frac{\mathrm{m(v-u)}}{t}$
According to the second law of motion, rate of change in an object's momentum is proportional to the applied force.
That is, F ∝ ma
or, F = kma
Here, k is a constant of proportionality. The value of k depends on the unit of force. Hence the unit of force is defined in such a way that the value of k becomes 1. When k is equal to 1, the above equation becomes
F = ma. And we are done with the deduction 😀

Example: Two boxes are side by side and in contact with each other. The first box has a mass of 2 kg, and the mass of the second box is 3 kg. Suppose they are pushed along a smooth floor by applying 2 N force to the first box.

1. Find the acceleration of the boxes.
2. Find the force exerted on the second box by the first box.

Why does a folded paper fall to the ground earlier than an unfolded paper dropped from a roof of the same height?

The folded papers surface area is small compared to the unfolded papers surface area. For this reason, the folded paper reaches the ground earlier because it encounters less air resistance on its way down, even though they start falling at the same time from the same height.

Rony has a mass of 40kg. He sets off for school with uniform acceleration of 0.4m/s from rest and reaches the school in 70 seconds. Rony's elder brother Jony has a mass of 50kg and the roof height of their house is 20 meters.

1. Find the distance of Rony's school.
2. Can Jony reach the roof carrying a mass of 10 kg by doing the same amount of work as Rony? Give your opinion.

1. A car's velocity increases uniformly from 10$\mathrm{ms}{}^{}$ to 25$\mathrm{ms}{}^{}$ in 5 seconds. Calculate the acceleration of the car.
2. A car's velocity decreases uniformly from 27$\mathrm{ms}{}^{}$ to 11$\mathrm{ms}{}^{}$ in 8 seconds. Calculate the deceleration of the car.
3. An acceleration of 1.5$\mathrm{ms}{}^{}$ is applied to a train moving at 72 km/h for 6 seconds. Calculate the final velocity and distance travelled.
4. A force applied to a toy car weighing 3.92N causes it to move with an acceleration of 0.5m/s on a floor having friction force of 0.5N.
   1. What is the value of the force acting on the car?
   2. Calculate the change in acceleration on the floor without friction?

Distance-Time Graph

• A horizontal line (a line parallel to x-axes) indicates no movement.
• A straight line indicates constant speed.
• An upward slope indicates rise in speed.
• A downward slope indicates fall in speed.
• Gradient of the distance-time graph gives speed.

Velocity-Time Graph

• The steepest section of the graph indicates the highest acceleration.
• Area under the velocity-time graph represents the displacement of an object.
• Gradient of the velocity-time graph gives acceleration.

Acceleration

Stopping Distance