How to Interpret Displacement-Time Graphs- Tutorial

What Is a Displacement-Time Graph?

A displacement-time graph shows how an object's position changes over time. The vertical axis represents displacement (usually in meters), and the horizontal axis represents time (usually in seconds).

That's it. Nothing complicated here. This graph tells you exactly where something is at any given moment, relative to its starting point.

The Slope Is Everything

Forget the shape of the curve. On a displacement-time graph, the slope is what matters. Slope equals velocity.

• Steep slope = high velocity
• Gentle slope = low velocity
• Horizontal line = not moving
• Curved line = changing velocity

You don't need to memorize complicated formulas. If you can estimate how steep a line is, you already know how fast something is moving.

Types of Motion on D-T Graphs

Stationary Object

A horizontal line means the object isn't moving. Displacement stays the same while time increases. The slope is zero, so velocity is zero.

Constant Velocity

A straight diagonal line means the object moves at a steady speed in one direction. The slope stays the same throughout because velocity doesn't change.

⚠️ Watch out: a straight line going downward still represents constant velocity. It's just moving in the negative direction. Many students get tripped up here.

Changing Velocity

A curved line means velocity is changing. The object is accelerating or decelerating. To find velocity at any specific point on a curve, draw a tangent line at that point and calculate its slope.

Positive vs. Negative Displacement

Displacement can be positive or negative depending on your reference point. If you set your starting position as zero, moving in your chosen positive direction gives positive values. Moving in the opposite direction gives negative values.

The graph doesn't lie. A line below the time axis means the object has passed its starting point and gone the other way.

Calculating Velocity: A Quick How-To

To find velocity from a displacement-time graph:

1. Pick two points on the line (or tangent)
2. Read their displacement values (y-axis)
3. Read their time values (x-axis)
4. Use: velocity = (change in displacement) ÷ (change in time)

Example: A car moves from 0m to 100m in 10 seconds.

Velocity = (100 - 0) ÷ (10 - 0) = 10 m/s

That's the entire calculation. No trigonometry needed unless the line is diagonal and you're working with actual graph coordinates.

Common Mistakes to Avoid

• Confusing with distance-time graphs: Distance-time graphs always go up. Displacement can go negative. Know which one you're working with.
• Ignoring the sign: Negative slope means negative velocity. It doesn't mean the object is slower.
• Reading the curve instead of the slope: A steep curve doesn't always mean high speed. Check the actual slope value.
• Forgetting units: Always include m/s or km/h. A number without units is useless in physics.

Comparing Motion Types

What the Graph Cannot Tell You

Displacement-time graphs show velocity through slope. They don't show acceleration directly. For acceleration, you need a velocity-time graph.

Also, this graph tells you nothing about the path taken. An object could move in a circle and return to the same point. The graph would show zero displacement at that moment, even though the object traveled a distance.

Practice Problem

Look at a graph showing a line from (0s, 0m) to (5s, 20m), then horizontal to (10s, 20m).

First segment: velocity = 20m ÷ 5s = 4 m/s

Second segment: velocity = 0m ÷ 5s = 0 m/s

The object moved at 4 m/s for 5 seconds, then stopped. Simple.

Final Point

Displacement-time graphs are straightforward once you focus on slope. Don't overthink the curves or the math. If you can draw a line and estimate its steepness, you can interpret these graphs.