The Story in the Graph
s–t and v–t: slope and area tell everything
What this lesson covers
Why it matters
A motion graph is a biography: every slope is a speed, every flat is a rest, every curve is a change of heart. Learn to read it, and no numerical can hide from you.
The idea in plain words
How to read motion graphs. Tap the rules.
s–t: slope = v · v–t: slope = a, area = s
A v–t graph is flat at 20 m/s for 5 s. Distance from the graph?
100 m — matching your cart's final s
- read velocity: s–t slope — steeper = faster; flat = at rest; curved = accelerating
- read acceleration: v–t slope — the acceleration; flat v–t = uniform velocity
- read distance: v–t area — area under the line = displacement — the second great trick
- area = 20 × 5 (a rectangle)
Predict first
On a displacement–time graph, a STRAIGHT sloped line means…
Slope of s–t IS velocity. Constant slope, constant velocity. A CURVING s–t line is where acceleration hides.
- uniform velocity (constant slope = constant speed) — correct
- acceleration
- the body is climbing a hill
What you do
Drive the cart one second at a time and lay your trace exactly on the 20 m/s target line.
Check yourself
A horizontal line on an s–t graph means…
Position unchanging as time passes = parked. (Flat on a v–t graph is the steady-motion one.)
On a v–t graph, the area under the curve gives…
velocity × time = displacement, strip by strip — the area trick derives all three equations of motion.
An s–t graph can never be…
A vertical jump means covering distance in ZERO time — infinite speed. Physics declines.
- the body is at rest — correct
- uniform velocity
- free fall
- displacement — correct
- acceleration
- nothing physical
- vertical (that would be teleportation) — correct
- curved
- flat