Key Points

An object is in motion when its position changes with time relative to a fixed reference point, also known as the origin.

Distance is the total path length covered and is a scalar quantity. Displacement is the shortest distance between the initial and final positions and is a vector quantity.

Displacement can be zero even if the distance covered is not zero. This occurs when an object returns to its starting position.

An object is in uniform motion if it covers equal distances in equal time intervals. It is in non-uniform motion if it covers unequal distances in equal time intervals.

Speed is the rate of change of distance, calculated as $v = \frac{s}{t}$. Average speed is the total distance travelled divided by the total time taken.

Velocity is the rate of change of displacement, or speed in a specific direction. For uniform acceleration, average velocity is the arithmetic mean of initial (u) and final (v) velocities: $v_{av} = \frac{u+v}{2}$.

Acceleration is the rate of change of velocity over time. The formula is $a = \frac{v-u}{t}$, and its SI unit is meters per second squared ($\text{m/s}^2$).

An object has uniform acceleration if it travels in a straight line and its velocity changes by equal amounts in equal intervals of time. An example is a freely falling body.

For uniform motion, the distance-time graph is a straight line. For non-uniform motion, it is a curve. The slope of the graph gives the speed.

For uniform velocity, the graph is a line parallel to the time axis. For uniform acceleration, it is a straight line with a constant slope. The slope represents acceleration.

The area enclosed by the velocity-time graph and the time axis represents the magnitude of the displacement of the object.

This equation relates final velocity (v), initial velocity (u), acceleration (a), and time (t). It is given by $v = u + at$.

This equation relates distance (s), initial velocity (u), time (t), and acceleration (a). It is given by $s = ut + \frac{1}{2}at^2$.

This equation relates final velocity (v), initial velocity (u), acceleration (a), and distance (s). It is given by $2as = v^2 - u^2$.

When an object moves in a circular path with uniform speed, its motion is called uniform circular motion. It is an accelerated motion because the direction of velocity changes continuously.

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