Difference Between Displacement-Time and Velocity-Time Graphs
Displacement and Velocity Time Graphs are essential tools in JEE Main Physics for analyzing motion visually and solving kinematics numericals quickly. These graphs transform mathematical equations into interpretable shapes, letting you see at a glance how an object moves with time. By understanding how to read, sketch, and compare these motion graphs, you build a strong foundation for tackling questions in kinematics, uniform and non-uniform motion, and acceleration. This article covers core meanings, proven techniques, worked examples, and practical insights tailored for JEE students.
What Are Displacement and Velocity Time Graphs?
A displacement-time graph plots an object's position (displacement, s) versus time (t). The graph’s slope at any point gives the object’s velocity. A velocity-time graph shows velocity (v) on the vertical axis and time on the horizontal axis—the slope here indicates acceleration, and the area under the curve gives displacement. Both types directly support JEE motion analysis and help visualize how quantities change over time.
- Displacement and velocity time graphs are key in motion in one dimension.
- They simplify questions in kinematics and uniformly accelerated motion.
- Quickly extract physical quantities using slopes and areas.
- Practice via mock tests on kinematics for JEE.
Difference Between Displacement-Time and Velocity-Time Graphs
| Feature | Displacement-Time Graph | Velocity-Time Graph |
|---|---|---|
| Y-axis quantity | Displacement (s) | Velocity (v) |
| Slope meanings | Velocity | Acceleration |
| Area under curve | No direct physical meaning | Displacement |
| Graph shapes (uniform motion) | Straight line (constant slope) | Horizontal line |
| Exam focus | Concept clarity, basic velocity | Area analysis, acceleration, numericals |
- Explore related concepts at difference between distance and displacement.
How to Draw and Interpret Displacement and Velocity Time Graphs
To sketch a displacement-time graph for uniform motion, plot a straight line with constant positive or negative slope. Curved lines indicate acceleration or deceleration—steeper curves mean faster change in velocity. A flat (horizontal) line shows zero velocity (object at rest).
- Mark time (t) on X-axis, displacement (s) on Y-axis.
- Plot known values at chosen time points.
- Join points smoothly for type of motion (straight for uniform, curve for non-uniform).
- Interpret slope: positive (forward), negative (backward), zero (stationary).
For velocity-time graphs, a straight horizontal line means constant velocity. A sloped line (up or down) means constant acceleration or deceleration. Complex curves show changing acceleration. The area under the graph gives displacement between two time intervals—a crucial skill for JEE.
Key Formulas and Example: Displacement and Velocity Time Graphs
- Slope of displacement-time graph = velocity (v = Δs/Δt)
- Slope of velocity-time graph = acceleration (a = Δv/Δt)
- Area under velocity-time graph = displacement (Δs)
Let’s apply formulas with a sample problem:
Suppose a body moves with constant velocity v = 3 m/s for 5 s. The velocity-time graph is a straight horizontal line at 3. The area under the graph = velocity × time = 3 × 5 = 15 m. This is the displacement in the time interval.
For accelerated motion: if a velocity-time graph ramps up linearly from 0 to 10 m/s in 4 s, area is a triangle = (1/2) × 4 × 10 = 20 m. That’s the total displacement covered.
- Practice advanced graphs via motion in 2D dimensions.
- Revise key ideas at kinematics revision notes.
Common Pitfalls and Applications in JEE: Displacement and Velocity Time Graphs
Common student mistakes include misreading slopes or neglecting negative areas (for motion in the opposite direction). Always pay attention to axes, sign convention, and units. Don’t confuse area under a displacement-time graph (which has no direct meaning) versus a velocity-time graph (where it is displacement).
- Negative slope in displacement-time graph: motion in reverse direction.
- Flat line in velocity-time graph: zero acceleration.
- Zero area under v-t graph: object returns to start position.
- Test yourself using kinematics mock test and important questions for JEE.
You’ll use these graphs for problems in laws of motion, projectile motion, and to compare motion types in JEE Main pattern questions. Vedantu’s Physics faculty has deep experience interpreting these graph types, especially from past year JEE questions.
- Expand skills by studying graphical analysis of kinematics.
- See multi-graph comparisions at displacement velocity and acceleration time graphs.
Related Motion Graphs, Practice, and What’s Next
- Study motion in one dimension for linear graphs and equations.
- Learn about average velocity formula in context.
- Tackle kinematics practice papers for exam prep.
- See real world applications at laws of motion page.
- Advance to complex graph reading at motion in 2D dimensions.
- For formula recap, visit Physics formulas for JEE Main.
- Understand foundational ideas at kinematics.
- Compare to uniform and non-uniform motion.
- Practice using kinematics mock test 1.
- Review common errors via graphical analysis of kinematics.
Mastering displacement and velocity time graphs arms you with a visual approach to kinematics, supporting all levels of JEE Main Physics. Consistent practice and clear understanding make you exam ready—Vedantu’s topic guides and tests are a helpful next step for deeper mastery.
FAQs on Displacement and Velocity-Time Graphs: Concepts, Differences & Application
1. How do you find displacement from a velocity-time graph?
Displacement from a velocity-time graph is found by calculating the area under the curve between the two time points.
To do this:
- Draw vertical lines at the start and end time on the graph.
- Find the area between the velocity curve and the time axis. For straight-line (constant velocity), it is a rectangle (Area = velocity × time). For non-uniform velocity, split into triangles/rectangles or use calculus.
- Area above time axis = positive displacement; below time axis = negative displacement.
2. What is the main difference between a displacement-time and velocity-time graph?
Displacement-time and velocity-time graphs represent different aspects of motion in Physics.
- Displacement-time graph: The slope gives velocity. A straight line means uniform velocity; a curve means changing velocity.
- Velocity-time graph: The slope gives acceleration. Area under the graph gives displacement.
3. How do you draw a displacement-time graph for uniform motion?
To draw a displacement-time graph for uniform motion (constant velocity):
- Plot time on the x-axis and displacement on the y-axis.
- Mark the starting point (usually at origin or a given value).
- Since velocity is uniform, draw a straight line with a constant, non-zero slope (not horizontal).
- The slope of this line gives the value of constant velocity.
4. What is the meaning of the slope of a velocity-time graph?
The slope of a velocity-time graph represents the acceleration of the object.
- Positive slope: Object is accelerating forwards.
- Negative slope: Object is decelerating or accelerating in reverse.
- Zero slope: Velocity is constant; acceleration is zero.
5. Are displacement-time and velocity-time graphs the same?
No, displacement-time and velocity-time graphs are not the same.
- Displacement-time graph: Shows how position changes over time; slope gives velocity.
- Velocity-time graph: Shows how velocity changes; slope gives acceleration; area under curve gives displacement.
6. Can a velocity-time graph ever be a horizontal line? What does it mean?
Yes, a velocity-time graph can be a horizontal line. This means the object has a constant velocity.
- Horizontal line above x-axis: Moving forwards at constant positive velocity.
- Horizontal line below x-axis: Constant negative velocity (moving backwards).
7. If the displacement-time graph is curved, what does this tell us about the motion?
A curved displacement-time graph indicates non-uniform motion (velocity is changing).
- The steeper the curve, the higher the instantaneous velocity.
- If the curve bends upward, velocity is increasing (acceleration).
- If it bends downward, velocity is decreasing (deceleration).
8. Are negative slopes possible in these graphs and what do they represent?
Yes, negative slopes are common in both types of motion graphs.
- Negative slope in displacement-time graph: Object is moving in the reverse direction (negative velocity).
- Negative slope in velocity-time graph: Object is decelerating or accelerating in the reverse direction (negative acceleration).
9. How can you avoid common mistakes in interpreting motion graphs in exams?
To avoid mistakes with motion graphs in exams:
- Follow proper axis labels: time on x-axis, displacement/velocity on y-axis.
- Remember what the slope and area represent for each graph type.
- Double-check units and sign (positive/negative slopes).
- Read the question carefully to find what is being asked (displacement, velocity, or acceleration).
- Practice with solved examples and MCQs from your textbook and previous years’ papers.
10. What is the formula for displacement using a velocity-time graph?
The displacement from a velocity-time graph is the total area under the velocity-time curve between two time points.
- For constant velocity (straight line): Displacement = velocity × time interval
- For varying velocity: Displacement = Sum of individual areas (rectangle/triangle)
- Mathematical form: Displacement = ∫ v(t) dt (definite integral if calculus is needed)
