Position-Time and Velocity-Time Graphs
Graphical representation in which the slope of x-t gives velocity, the slope of v-t gives acceleration and the area under v-t gives displacement.
What is Position-Time and Velocity-Time Graphs?
Graphical representation in which the slope of x-t gives velocity, the slope of v-t gives acceleration and the area under v-t gives displacement.
Key formula / rule: Slope of x-t = v; slope of v-t = a; signed area under v-t = displacement.
Key points
- Interpret slopes and areas of motion graphs.
- Construct the v-t graph corresponding to a described motion.
Common exam trap
Taking area under v-t as distance when part of it lies below the axis.
Definitions
- Term
Position-Time and Velocity-Time Graphs
- Meaning
Graphical representation in which the slope of x-t gives velocity, the slope of v-t gives acceleration and the area under v-t gives displacement.
- Term
Position-Time and Velocity-Time Graphs — explanation
- Meaning
Graphs let a student read a whole motion at a glance and solve problems where the algebraic route is clumsy. Signed area matters: area below the time axis is negative displacement.
Learning objectives
Interpret slopes and areas of motion graphs.
Construct the v-t graph corresponding to a described motion.
Formulae
- Key point
Slope of x-t = v; slope of v-t = a; signed area under v-t = displacement.
- Key point
Area magnitude summed without sign gives distance.
- Key point
A curved x-t graph implies non-zero acceleration.
Prerequisites
PHY-U1-KIN-T1-S2-C1
Common mistakes
Taking area under v-t as distance when part of it lies below the axis.
Reading intercepts as slopes.
Keywords
Position-Time
Velocity-Time
Graphs
Practice preview
What does the slope of a position-time (x-t) graph represent?…
easy
What does the area under a velocity-time (v-t) graph represent?…
easy
What does the slope of a velocity-time (v-t) graph represent?…
easy