Solution of Motion

Motion is the change in position of an object with respect to its surroundings in a certain period of time. It can be described in terms of distance, displacement, speed, velocity, and acceleration. The solution of motion problems involves the use of mathematical equations and formulas.

Distance and Displacement

Distance is the total length covered by an object in its motion, while displacement is the change in position of an object from its initial to final position. Displacement is a vector quantity and has both magnitude and direction.

Speed and Velocity

Speed is the rate at which an object covers a distance, while velocity is the rate at which an object changes its displacement. Velocity is a vector quantity and has both magnitude and direction.

Acceleration

Acceleration is the rate at which an object changes its velocity. It is a vector quantity and has both magnitude and direction. The acceleration of an object can be calculated as the change in velocity divided by the time taken.

Equations of Motion

The equations of motion are mathematical formulas that describe the motion of an object in terms of its initial velocity, final velocity, acceleration, displacement, and time taken. These equations are:

- v = u + at
- s = ut + 1/2 at^2
- v^2 = u^2 + 2as
- s = 1/2 (u + v) t

where u is the initial velocity, v is the final velocity, a is the acceleration, s is the displacement, and t is the time taken.

Example Problem

A body travels 200 cm in 2 seconds with a constant acceleration of 20 cm/s^2. Find its initial and final velocity.

Solution:

Given, distance = 200 cm, time taken = 2 s, acceleration = 20 cm/s^2

Using the equation, s = ut + 1/2 at^2, we can find the initial velocity.

s = ut + 1/2 at^2
200 = u(2) + 1/2 (20)(2)^2
200 = 2u + 40
2u = 160
u = 80 cm/s

Using the equation, v = u + at, we can find the final velocity.

v = u + at
v = 80 + (20)(2)
v = 120 cm/s

Therefore, the initial velocity is 80 cm/s and the final velocity is 120 cm/s.

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