Velocity

The mathematical relationship for average velocity is expressed as the change in displacement divided by the time taken. This is represented by the formula: $v = \frac{\Delta s}{\Delta t}$ where $v$ is velocity, $\Delta s$ is change in displacement, and $\Delta t$ is the time interval.

In one-dimensional motion, direction is often indicated using algebraic signs. A positive value typically indicates motion in a chosen 'forward' direction, while a negative value indicates motion in the opposite 'backward' direction.

Velocity is fundamentally linked to the concept of resultant force. According to Newton's First Law, an object will maintain a constant velocity (including a velocity of zero) unless acted upon by an unbalanced external force.

Constant Speed vs. Constant Velocity: An object moving in a circle at a steady $10 m/s$ has constant speed but changing velocity because its direction of travel is continuously rotating.

Distance vs. Displacement: If a runner completes one full lap of a $400 m$ track, their distance is $400 m$, but their displacement is $0 m$. Consequently, their average speed is positive, but their average velocity for the full lap is zero.

Check the Units: Always ensure time is in seconds and displacement is in metres before calculating velocity to avoid power-of-ten errors. If given $km/h$, multiply by $\frac{1000}{3600}$ to convert to $m/s$.

Direction Matters: In written answers, never provide just a number for velocity. Always include a direction (e.g., 'forward', 'to the right', or a bearing) unless the question specifically asks for the magnitude.

Interpret the Sign: If a calculation results in a negative velocity, it means the object is moving in the opposite direction to what was defined as positive. It does NOT necessarily mean the object is slowing down.

Graph Sanity Check: On a velocity-time graph, a horizontal line above the x-axis represents constant velocity in the positive direction. A horizontal line on the x-axis means the object is stationary ($v = 0$).

Confusing Velocity with Acceleration: Students often think that a high velocity means a high acceleration. In reality, an object can have a very high velocity (like a jet at cruise) while having zero acceleration.

The 'Zero Velocity' Trap: Many assume that if an object returns to its starting point, its motion was 'nothing'. While the average velocity is zero, the instantaneous velocity at any point during the trip was likely non-zero.

Negative Velocity vs. Deceleration: Negative velocity simply indicates direction. Deceleration (slowing down) occurs only when the acceleration vector is in the opposite direction to the velocity vector.

Terminal Velocity: This is a specific case where an object falling through a fluid reaches a constant velocity because the upward drag force perfectly balances the downward gravitational force.

Relative Velocity: This concept explains how velocity appears different to observers in different frames of reference, such as a person walking on a moving train.

Momentum: Velocity is a critical component of momentum ($p = mv$). Because velocity is a vector, momentum is also a vector, which is vital for calculating outcomes in collisions.