Revision summary

State the body, origin, positive direction, interval and model. Keep signed motion quantities distinct from their magnitudes.

Motion quantities

Position and displacement

Position is relative to an origin. Displacement over an interval is final position minus initial position.

Distance and speed

Distance is total path length. Average speed = total distance / elapsed time. Instantaneous speed is the magnitude of velocity.

Velocity and acceleration

Average velocity = displacement / elapsed time. Average acceleration = Δv/Δt. Locally, v = dx/dt and a = dv/dt.

In one dimension, opposite velocity and acceleration signs mean slowing; matching signs mean increasing speed. Zero velocity at a turning instant need not mean zero acceleration.

Graph meanings

• Position-time or displacement-time gradient: velocity. A chord gives an interval average; a tangent gives a local value.
• Cumulative distance-time gradient: speed. Cumulative distance does not decrease.
• Velocity-time gradient: acceleration.
• Signed velocity-time area: displacement. Add area magnitudes, or use speed-time area, for distance.
• For a curved graph, estimate local gradients and areas with suitable intervals. Report numerical area approximations as estimates.

Straight-line constant acceleration

Derive these from constant acceleration and the signed area of a straight velocity-time graph. All variables refer to the same interval. A reversal is allowed, but s is displacement, not automatically total distance.

For vertical motion with upward positive and negligible air resistance, use a = -g throughout flight. Select velocity roots using direction and time roots using the stated time domain. The acceleration remains downward when velocity is zero at the top.

Inertia and momentum

Mass measures resistance to a change in motion. Momentum p = mv is a vector; Δp = p_final - p_initial. Its units satisfy N s = kg m/s.

All three Newton laws

1. First: a body stays at rest or at constant velocity unless a resultant external force acts.
2. Second: momentum-change rate is proportional to the resultant force and in its direction. In SI, F_resultant = dp/dt; interval-average force = Δp/Δt.
3. Third: interaction partners have equal magnitude and opposite direction, act simultaneously and act on different bodies.

Balanced forces on one body are not automatically a third-law pair. Equal forces on different masses can produce different accelerations.

Use force and data models

For constant mass, F_resultant = ma. Add the actual forces first; a resultant arrow is their summary. A constant resultant and constant mass justify constant acceleration.

Successive position differences divided by their actual time intervals give interval-average velocities. For constant acceleration, plot them at midpoint times; fit velocity against time to estimate acceleration and initial velocity. Preserve raw data and match any claimed precision to the measurement method.

The spreadsheet exercise and downloads cover XLSX/CSV input, manual entry, copied formulas and formatting, a displayed linear trendline, trapezoidal areas and a local-gradient estimate.

Symbols depend on context. Here x is position, s is displacement over an interval, and u and v are its initial and final velocities. Other contexts may use w or c for a speed or velocity; read the definition rather than inferring the quantity from the letter alone.