Linear Motion Quiz

Distance

• Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

• Scalars are quantities that are fully described by a magnitude (or numerical value) alone.

Displacement

• Displacement is a vector quantity that refers to the distance from the original/starting point to the end-point: it is the object's overall change in position.

• Vectors are quantities that are fully described by both a magnitude and a direction. 

Speed Equation: S = D/T - m/s

S = Distance/Time

Acceleration Equation A = (V - U/T)  - m/s²

Acceleration = (Final - Initial)/Time

Linear Velocity Equation V = 🔺S/🔺T  - m/s north, south, east, west

Velocity = Displacement/Time

Speed vs Velocity vs Acceleration

Speed is how fast an object is moving, while velocity includes both its speed and direction. Acceleration is the rate at which velocity changes, meaning it can be a change in speed, direction, or both. 

Acceleration (Understanding Negative Acceleration)

• Acceleration is the rate of change of velocity over time

• It tells you how quickly an object speeds up, slows down, or changes direction. 

• If velocity is changing—faster, slower, or changing direction—there is acceleration. 

Position vs Time Graph

• A position vs. time graph plots an object’s position on the vertical axis and time on the horizontal axis to visually represent its motion.

• The slope of this graph indicates the object's velocity: a steeper slope means faster velocity, a positive slope means movement in the positive direction, and a negative slope means movement in the negative direction.

• A horizontal line signifies that the object is at rest (zero velocity), and a curved line indicates that the object is accelerating, as its velocity is changing. 

• Slope equals velocity: The slope of the line connecting two points on the graph represents the object's average velocity over that time interval. For instantaneous velocity, find the slope of the line tangent to the curve at a specific point.

  Horizontal line: If the line is flat (slope is zero), the object is not moving; its position is constant over time.

  Straight line: A straight line shows that the object is moving at a constant velocity.

  Curved line: A curved line indicates acceleration, meaning the object's velocity is changing. The steepness of the curve shows the magnitude of the velocity, while the direction of the curve (concave up or down) indicates positive or negative acceleration.

Velocity vs Time Graph

• A velocity vs. time graph plots velocity on the y-axis against time on the x-axis, where the slope represents acceleration and the area under the curve represents displacement. 

• A steeper slope indicates greater acceleration, a horizontal line shows constant velocity (zero acceleration), and a downward slope signifies deceleration or negative acceleration.

• The area under the curve quantifies the total change in position, as multiplying velocity by time results in displacement. 

• Slope: The slope of the line at any point is the acceleration.

  Positive slope: The object is speeding up (positive acceleration).

  Zero slope (horizontal line): The object is moving at a constant velocity (zero acceleration).

  Negative slope: The object is slowing down or accelerating in the negative direction.

  Steeper slope: Indicates a greater acceleration.

  Area under the curve: The area between the line and the time axis represents displacement.

  Area above the x-axis: Represents positive displacement (movement in the positive direction).

  Area below the x-axis: Represents negative displacement (movement in the negative direction).

Acceleration Examples

Velocity

Acceleration

What direction is acceleration?

What happens?

Examples

+

+

same direction

speeds up

A sprinter running (+) and still accelerating forward (+)

+

–

opposite direction

slows down

A runner moving forward (+), but slowing down as they approach a finish line (acceleration is backward, so -).

–

–

same direction

speeds up (backward)

A basketball player running backwards (-) and pushing harder to go faster backwards (-).

–

+

opposite direction

slows down (while moving backward)

A soccer player jogging backward (-) and slowing down to stop (accelerating is forward, so +).