➡️ Motion in a Straight Line

1. Rest and Motion

Motion is relative. An object is in motion if it changes its position with respect to its surroundings with time.

Distance: Total path length covered. It is a scalar quantity. Always positive.

Displacement: Shortest distance between initial and final position. It is a vector quantity. Can be positive, negative, or zero.

Speed is the rate of change of distance. (Scalar: v = d/t)

Velocity is the rate of change of displacement. (Vector: v = Δx/Δt)

It is the velocity of an object at a specific instant of time. Mathematically, it is the derivative of position with respect to time: v = dx/dt.

When an object moves with a constant acceleration 'a', we use these three magical equations:

v = u + at
s = ut + ½ at²
v² = u² + 2as Where: u = initial velocity, v = final velocity, a = acceleration, s = displacement, t = time.

Position-Time Graph: Slope gives Velocity.
Velocity-Time Graph: Slope gives Acceleration. Area under the curve gives Displacement.
Acceleration-Time Graph: Area under the curve gives change in Velocity.