1D Kinematics Key Concepts: Vectors, Scalars, Graphs, and Free Fall

Vector quantity

A quantity with both magnitude and direction.

Scalar quantity

A quantity with magnitude only.

Distance and displacement equality

When the motion is along a straight path with no change in direction.

Displacement if you finish where you started

Zero (but distance is non-zero).

Difference between speed and velocity

Speed is scalar (how fast); velocity is vector (rate & direction).

Average velocity can be zero

Yes, if you return to your starting point.

Acceleration

The rate of change of velocity (magnitude or direction).

Object accelerating at constant speed

Yes, if its direction changes (e.g., in circular motion).

Negative acceleration

The object's velocity is decreasing (slowing down).

Slope of a position-time graph

Velocity.

Straight diagonal line on a position-time graph

Constant velocity.

Curved line on a position-time graph

Changing velocity (acceleration).

Slope of a velocity-time graph

Acceleration.

Area under a velocity-time graph

Displacement.

Horizontal line at zero velocity on a v-t graph

The object is at rest.

Line with a negative slope on a v-t graph

The object's velocity is decreasing (negative acceleration).

Free fall

Motion under the influence of gravity alone.

Acceleration of a free-falling object near Earth

Approximately 9.8 m/s² downward, regardless of mass.

Thrown object at the top of its path

Its velocity is zero, but acceleration is still downward.

Acceleration of 0 m/s²

The object is either at rest or moving at constant velocity.