Vectors, Motion, and Kinematics

Manual: General · Subject: Applied Physics

Analyze motion in one and two dimensions using vector reasoning, graphs, and kinematic equations.

Scalars and Vectors

Vector basics

Scalars have magnitude only, while vectors have magnitude and direction. Displacement, velocity, acceleration, and force are vectors, so direction must be tracked carefully in applied problems.

Scalar vs vector

Scalar

Described by magnitude only
Examples: temperature, mass, speed

Vector

Described by magnitude and direction
Examples: displacement, velocity, force

ℹ️

Coordinate choice

Choose axes that simplify the motion. In projectile motion, horizontal and vertical components can often be solved independently.

Constant-Acceleration Motion

Kinematic equations

For constant acceleration, the equations $v = v_0 + at$ , $x = x_0 + v_0 t + \frac{1}{2}at^2$ , and $v^2 = v_0^2 + 2a(x-x_0)$ allow prediction of position and speed without directly modeling the forces.

If an object moves with constant positive acceleration, which statement must be true?

Its velocity is always increasing in magnitude Its position must be positive Its speed always increases Its velocity changes by equal amounts in equal times

What is the difference between speed and velocity?

Graphs and Interpretation

Reading graphs

A slope on a position-time graph gives velocity, and a slope on a velocity-time graph gives acceleration. The area under a velocity-time graph gives displacement.

Graph relationships

Graph	Slope means	Area means
Position vs time	Velocity	No common direct interpretation
Velocity vs time	Acceleration	Displacement
Acceleration vs time	Jerk change rate	Change in velocity

What does the area under a velocity-time graph represent?

Acceleration Displacement Force Momentum

Why is vector decomposition useful in projectile motion?

Neuroanatomy Explorer

Memory Deck

Match the Pairs

Concept Constellation