Key Points

An object is in motion if its position changes with time relative to a fixed reference point. If its position does not change, the object is said to be at rest.

Distance is the total path length covered by an object and is a scalar quantity. Displacement is the shortest straight-line distance between the initial and final positions and is a vector quantity.

Scalar quantities are physical quantities specified only by their magnitude, like distance and speed. Vector quantities require both magnitude and direction, like displacement and velocity.

Average speed is the total distance traveled by an object divided by the total time taken. The formula is $\text{average speed} = \frac{\text{total distance}}{\text{time interval}}$.

Average velocity is the displacement of an object divided by the total time interval. The formula is $\text{average velocity} = \frac{\text{displacement}}{\text{time interval}}$.

Acceleration is the rate of change of velocity over time. The formula is $a = \frac{v - u}{t}$, where $v$ is the final velocity and $u$ is the initial velocity. Its SI unit is $\text{m/s}^2$.

An object in uniform motion travels equal distances in equal time intervals, meaning its velocity is constant. In non-uniform motion, it travels unequal distances in equal time intervals, meaning its velocity changes.

For a position-time graph, the slope represents the velocity of the object. A straight line indicates uniform velocity, while a curved line indicates non-uniform velocity (acceleration).

For a velocity-time graph, the slope represents acceleration, and the area under the graph represents the displacement. A straight line parallel to the time axis indicates zero acceleration.

The first kinematic equation relates final velocity ($v$), initial velocity ($u$), acceleration ($a$), and time ($t$). The equation is $v = u + at$.

The second kinematic equation relates displacement ($s$), initial velocity ($u$), time ($t$), and acceleration ($a$). The equation is $s = ut + \frac{1}{2}at^2$.

The third kinematic equation relates final velocity ($v$), initial velocity ($u$), acceleration ($a$), and displacement ($s$). The equation is $v^2 = u^2 + 2as$.

When an object moves in a circular path with a constant speed, its motion is called uniform circular motion. Although the speed is constant, the velocity is continuously changing due to the change in direction.

An object in uniform circular motion is considered to be accelerating because the direction of its velocity is constantly changing at every point along the path.

The speed of an object in uniform circular motion can be calculated using the formula $v = \frac{2\pi R}{T}$, where $R$ is the radius of the circular path and $T$ is the time taken for one complete revolution.