8.15: Position, Displacement, Velocity, and Graphs

Practice flashcards covering position, displacement, distance, origin, velocity (average and instantaneous), speed vs. velocity, slopes on position-time graphs, and the relationship between velocity-time graphs and displacement.

What is position in one-dimensional motion?

Position is the location along the axis (the x-axis) defined relative to an origin; it can be positive or negative depending on direction.

What is displacement (Δx)?

Displacement is the change in position: Δx = xfinal − xinitial; it depends only on start and end positions, not the path taken.

What is distance traveled?

Distance is the total length of the path traveled; it is always nonnegative and does not depend on direction.

What is an origin and why is it chosen?

Origin is the reference point where position is defined as zero; you can choose any origin, and the physics of motion remains the same.

How do you determine xfinal and xinitial in a problem?

xfinal is the position at the end of the interval along the x-axis; xinitial is the position at the start.

What is average velocity?

Average velocity is the displacement divided by the time interval: v_avg = Δx/Δt; it depends only on start, end, and total time.

What is instantaneous velocity?

Instantaneous velocity is the velocity at a specific moment; on a position-time graph, it is the slope at that moment.

What is the difference between speed and velocity?

Speed is the magnitude of velocity (how fast); velocity includes both speed and direction (sign in 1D).

How do you obtain velocity from a position-time graph?

The velocity is given by the slope (rise over run) of the graph; this slope equals the average velocity over the chosen interval.

What does a straight-line position-time graph indicate?

A constant velocity; the slope is constant, meaning velocity does not change over time.

What do rise and run represent on a position-time graph?

Rise corresponds to displacement Δx; run corresponds to time interval Δt; slope equals Δx/Δt, i.e., average velocity.

Why choose the origin smartly in problems?

Choosing a convenient origin can simplify numbers without changing the physics of the motion.

What is Δt?

Δt is the time interval between start and end times, i.e., tfinal − tinitial.

What is the area under a velocity-time graph?

The area under a velocity-time graph equals the displacement Δx over the interval.

What does the sign of velocity indicate in one dimension?

The sign indicates direction along the axis: positive for one direction, negative for the opposite.

How can you choose easy triangles to compute slope on a graph?

Use small, round-number segments (easy rise and run) so the slope calculation is straightforward and accurate.

If you end where you started (Δx = 0) what is the average velocity?

Zero; v_avg = Δx/Δt = 0/Δt = 0.

When is instantaneous velocity equal to average velocity?

If the motion has constant velocity, the instantaneous velocity equals the (constant) average velocity over any interval.