A velocity vs time graph plots an object's velocity (y-axis) against time (x-axis); the slope of the line gives the object's acceleration, and the area between the curve and the time axis gives the object's displacement (Topic 1.2, Representations of Motion).
A velocity vs time graph (often written v-t graph) shows how fast an object is moving, and in what direction, at every moment in time. Velocity goes on the y-axis, time on the x-axis. That setup packs three pieces of information into one picture. The height of the curve tells you the velocity at that instant. The slope tells you the acceleration, because slope is rise over run, which here is Δv/Δt, exactly the definition of average acceleration in the CED (1.2.B.3). The area between the curve and the time axis tells you the displacement, because velocity times time is distance covered.
Reading the sign matters as much as reading the number. A curve above the time axis means the object moves in the positive direction; below the axis means the negative direction. When the curve crosses the time axis, the object's velocity is momentarily zero, which usually means it's turning around. A horizontal line means constant velocity (zero slope, zero acceleration). A straight tilted line means constant acceleration. None of this tells you where the object is, only how it's moving. To get position you need the area, or a position vs time graph.
This graph lives in Topic 1.2 (Representations of Motion) in Unit 1: Kinematics, and it directly supports learning objective 1.2.B, describing the average velocity and acceleration of an object. The CED defines average velocity as Δx/Δt and average acceleration as Δv/Δt (1.2.B.2 and 1.2.B.3), and the v-t graph is where those definitions become visual. Acceleration is literally the slope you can measure with a ruler, and displacement is literally the area you can count in grid squares. The CED also says an object accelerates if the magnitude OR direction of its velocity changes (1.2.B.4), and a v-t graph makes that visible. Any non-horizontal segment means acceleration, even while the object is slowing down or reversing. Because every later unit (forces, energy, momentum) builds on describing motion, being fluent with this graph pays off across the whole course.
Keep studying AP Physics 1 Unit 1
Position vs Time Graph (Unit 1)
These two graphs are linked by slope. The slope of a position vs time graph IS the velocity, so the v-t graph is basically a plot of the x-t graph's slope at every moment. A curved x-t graph becomes a tilted straight line on a v-t graph.
Acceleration (Unit 1)
Acceleration is the slope of the v-t graph, straight from the CED equation a_avg = Δv/Δt (1.2.B.3). A steep line means a big acceleration, a horizontal line means zero acceleration, and a downward slope means acceleration in the negative direction (which is not the same thing as slowing down).
Constant Velocity (Unit 1)
Constant velocity shows up as a flat horizontal line on a v-t graph. That flat line is also your visual cue for zero net force once you reach Unit 2, so recognizing it now sets up Newton's first law later.
Free Fall and Acceleration due to Gravity (Unit 1)
An object in free fall has a v-t graph that is a straight line with slope g (about 9.8 m/s² downward). For a ball thrown upward, the line crosses the time axis at the peak of the throw. The velocity hits zero there, but the slope (the acceleration) never changes.
Velocity vs time graphs show up constantly in Unit 1 multiple-choice questions. Typical stems ask you to find acceleration from the slope, find displacement from the area, identify when an object turns around (the curve crosses the time axis), or match a v-t graph to its corresponding x-t graph or a written description of motion. On free-response questions, kinematics graphs feed the experimental design and data analysis skills. You may be asked to sketch a v-t graph from data, extract a quantity from a given graph, or justify a claim about motion using graph features. The two moves you must be automatic with are slope = acceleration and area = displacement, and you should be ready to say which feature you used and why when justifying an answer.
Same axes layout, completely different meaning. On a position vs time graph, slope means velocity and the height tells you WHERE the object is. On a velocity vs time graph, slope means acceleration, height tells you how fast the object moves, and you need the AREA to find displacement. The classic trap is a v-t graph that crosses the time axis. On an x-t graph that would mean the object passed the origin, but on a v-t graph it means the object stopped for an instant and reversed direction. Always check the y-axis label before you interpret anything.
The slope of a velocity vs time graph equals the object's acceleration, matching the CED definition a_avg = Δv/Δt (1.2.B.3).
The area between the curve and the time axis equals the object's displacement; area below the axis counts as negative displacement.
A horizontal line on a v-t graph means constant velocity and zero acceleration, while a straight tilted line means constant acceleration.
When the curve crosses the time axis, the velocity is momentarily zero, which usually means the object is changing direction.
An object is accelerating whenever the v-t graph is not horizontal, even if the object is slowing down (1.2.B.4).
A negative slope does not automatically mean slowing down; an object moving in the negative direction with a negative slope is actually speeding up.
It shows an object's velocity at every moment, with velocity on the y-axis and time on the x-axis. The slope gives acceleration and the area under the curve gives displacement, both straight from the Topic 1.2 definitions of average velocity and acceleration.
Not necessarily. A negative slope means the acceleration points in the negative direction. If the velocity is positive, the object slows down, but if the velocity is already negative, the object is speeding up. Check whether velocity and acceleration have the same sign.
On a position vs time graph, the slope is velocity. On a velocity vs time graph, the slope is acceleration and the area under the curve is displacement. The same shape means totally different motion depending on the y-axis, so read the label first.
Calculate the area between the curve and the time axis using rectangles and triangles. Area above the axis is positive displacement, area below is negative, and you add them with their signs to get total displacement (Δx = x − x₀).
The object's velocity is zero at that instant, which usually means it stops momentarily and reverses direction, like a ball at the top of a throw. It does not mean the object returned to its starting position.