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Velocity Time Graphs - Definition, Example, FAQs

Velocity Time Graphs - Definition, Example, FAQs

Vishal kumarUpdated on 02 Jul 2025, 05:00 PM IST

Here, in this article, we will learn about the velocity time graph/vt graph, vt meaning, velocity time, what is velocity time graph, when the acceleration of a particle is increasing linearly, how to draw velocity time graph, what velocity time graph gives, velocity time graph examples, velocity time relation, velocity vs time graph/velocity versus time graph, constant velocity graph, study the velocity time graph and calculate acceleration, what we studied about velocity time graph class 9, the velocity time graph of a particle, velocity graph, velocity time graph acceleration, how to find acceleration in velocity time graph, zero acceleration graph, the velocity displacement graph of a particle, what does velocity time graph represent etc.

Velocity Time Graphs - Definition, Example, FAQs
Velocity Time Graphs

What is the Velocity time graph?

A velocity-time graph represents the different velocities of a moving object at different times. We can say that when an object moves with a speed in a particular direction, it is the velocity of that object. Velocity is a vector quantity as it has both direction and magnitude. The velocity-time graph gives the acceleration of an object. We know that acceleration is the rate of change of velocity. The vertical axis of the velocity-time graph is taken as the velocity of the object and horizontal axis as the time elapsed.

On the velocity- time graph, we get different types of acceleration. An object may have a constant velocity, increasing velocity, or decreasing velocity and it can easily be determined whether the object is accelerating, decelerating, or not accelerating at all.

If an object moves with a constant velocity, then we obtain a straight horizontal line on the graph. It means that there is no change in the velocity and as a result, we get no acceleration or zero acceleration.

If an object moves with an increasing velocity or constant acceleration, then we get a straight sloped line on the graph. Here, in this case the acceleration of a particle is increasing linearly.

If an object moves with an increasing acceleration, then we get curved lines.

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Let us study these cases one by one.

Case I:- Constant velocity graph or No Acceleration graph

If the object moves with constant velocity, it means that the initial and final velocity of the object remains the same. The slope obtained in this case will be constant. It leads us to conclude that there is no increase or no decrease in the acceleration of the object and the object will have zero acceleration in this case.

The following VT graph shows zero acceleration.

Constant velocity

Case II:- Increasing Velocity or Constant Acceleration

If the velocity of an object increases throughout its motion, then the final velocity becomes more than the initial velocity. The initial velocity, in this case, can be zero, as the object is constantly increasing its speed. The slope of the velocity-time graph obtained in this case will increase. It leads us to conclude that the body is in constant acceleration.

The following VT graph shows constant acceleration.

constant acceleration

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Case III:- Increasing rate of change of velocity or Increasing acceleration

If the rate of change of velocity increases throughout the motion, then the final velocity will be much more than the initial velocity. The initial velocity in this case can be zero as the acceleration of the object is increasing every second at some rate. The slope of the velocity-time graph in this case will lead us to conclude that the graph will form a curve. Hence, the curve in this slope has increasing/decreasing acceleration.

The following VT graph shows increasing acceleration.

increasing acceleration

We can obtain a decreasing velocity-time graph similar to the increasing velocity-time graph. In this case the slope will decrease as the velocity is decreasing. Here, in this case we will get a negative slope and the acceleration will be decreasing.

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Commonly Asked Questions

Q: What is a velocity-time graph?
A:
A velocity-time graph is a visual representation that shows how an object's velocity changes over time. The vertical axis represents velocity, while the horizontal axis represents time. This graph helps us understand an object's motion, including whether it's speeding up, slowing down, or moving at a constant speed.
Q: How can you tell if an object is at rest from a velocity-time graph?
A:
An object is at rest when its velocity is zero. On a velocity-time graph, this would be represented by a horizontal line along the time axis (where velocity = 0). If this line extends for a period of time, it means the object remains at rest for that duration.
Q: What's the difference between speed and velocity on a velocity-time graph?
A:
While both speed and velocity are related to how fast an object is moving, velocity includes direction. On a velocity-time graph, the magnitude of velocity represents speed, while the sign (positive or negative) indicates direction. Speed is always positive, but velocity can be positive, negative, or zero.
Q: What does a velocity-time graph look like for an object in free fall?
A:
For an object in free fall (ignoring air resistance), the velocity-time graph would be a straight line with a positive slope. The slope of this line represents the acceleration due to gravity (approximately 9.8 m/s² on Earth). The line starts at zero (or the initial velocity) and continues to increase linearly with time.
Q: What does the steepness of a velocity-time graph tell you?
A:
The steepness of a velocity-time graph indicates the magnitude of acceleration. A steeper slope means a greater acceleration (positive or negative), while a less steep slope indicates a smaller acceleration. A horizontal line (no steepness) means no acceleration.

Velocity time graph questions for class 9

Q.1 A particle starts from rest and moves with a uniform acceleration of 5m/s2 for 10s and then it moves with a constant velocity for 4s. Later it slows down and comes to rest in 5s. Draw the velocity graph for the motion of the body and answer the following questions:
a. What is the maximum velocity attained by the body?
b. What is the distance travelled during this period of acceleration?
c. What is distance travelled when the body is moving with constant velocity?
d. What is the retardation of the body while slowing down?
e. What is the distance travelled by retarding?
f. What is the total distance travelled?

Solution)

velocity graph for the motion of the body

(a) Maximum velocity will be reached when acceleration is stopped at the end of the first 10 sec and is shown in graph

V = 50 m/s
(b) Distance is given by the area of the graph enclosed till 10 sec

s = (1/2) X 50 X 10 = 250 m

(c) distance travelled when the body was moving with constant velocity is given by the enclosed graph from A to B

= 4 X 50 = 200m

(d) Retardation is given by the slope of the curve from B to C

A = (0-50)/5 = - 10 m/s2

(e) Distance = (1/2) X 50 X 5 =125m

(f) Total distance is given by the total area of the graph = 250 + 200 + 125 = 575 m

Also check-

NCERT Physics Notes:

Commonly Asked Questions

Q: How do you interpret the slope of a velocity-time graph?
A:
The slope of a velocity-time graph represents acceleration. A positive slope indicates positive acceleration (speeding up), a negative slope indicates negative acceleration (slowing down), and a horizontal line (zero slope) indicates constant velocity (no acceleration).
Q: What does the area under a velocity-time graph represent?
A:
The area under a velocity-time graph represents the displacement of the object. This is because displacement is the product of velocity and time, which corresponds to the area under the curve on a velocity-time graph.
Q: Can velocity be negative on a velocity-time graph?
A:
Yes, velocity can be negative on a velocity-time graph. A negative velocity indicates that the object is moving in the opposite direction to the one defined as positive. For example, if moving right is positive, then a negative velocity means the object is moving left.
Q: How do you determine if an object is accelerating from a velocity-time graph?
A:
An object is accelerating if the velocity-time graph is not a horizontal line. Any change in the graph's slope (either increasing or decreasing) indicates acceleration. A curved line also represents acceleration, as the velocity is continuously changing.
Q: What does a horizontal line on a velocity-time graph mean?
A:
A horizontal line on a velocity-time graph indicates that the object is moving at a constant velocity. This means the speed and direction of the object remain unchanged over that period of time, and there is no acceleration.

Frequently Asked Questions (FAQs)

Q: How do you represent the motion of a car braking to a stop on a velocity-time graph?
A:
A car braking to a stop would be represented by a line with a negative slope on a velocity-time graph. The line would start at the car's initial velocity and decrease to zero. The slope of this line represents the deceleration rate. If the braking is constant, the line will be straight. If the braking force varies, the line might be curved, with the slope becoming steeper as the car slows down.
Q: What does a velocity-time graph look like for a person walking, then running, then walking again?
A:
This velocity-time graph would have three distinct sections:
Q: How can you tell the difference between uniform motion and uniformly accelerated motion on a velocity-time graph?
A:
Uniform motion (constant velocity) is represented by a horizontal line on a velocity-time graph, as the velocity doesn't change over time. Uniformly accelerated motion is represented by a straight line with a non-zero slope, as the velocity is changing at a constant rate over time.
Q: What does a velocity-time graph look like for a ball rolling down a hill and then up another hill?
A:
This velocity-time graph would have three main sections:
Q: How do you represent the motion of a yo-yo on a velocity-time graph?
A:
A yo-yo's motion on a velocity-time graph would show a repeating pattern:
Q: What does a velocity-time graph look like for an object experiencing air resistance while falling?
A:
For an object falling with air resistance, the velocity-time graph would start with a steep negative slope (acceleration due to gravity), but this slope would gradually decrease as the air resistance increases. Eventually, the graph would approach a horizontal line, representing terminal velocity, where the force of air resistance equals the force of gravity.
Q: How can you determine the average acceleration from a velocity-time graph?
A:
The average acceleration can be determined from a velocity-time graph by calculating the slope of the line connecting the initial and final points of the interval in question. Mathematically, this is (final velocity - initial velocity) / (final time - initial time). Graphically, it's the slope of the straight line from the start point to the end point of the interval.
Q: What does a velocity-time graph look like for an object in simple harmonic motion?
A:
For an object in simple harmonic motion, like a mass on a spring, the velocity-time graph would be a cosine or sine curve. The velocity oscillates between positive and negative values, representing back-and-forth motion. The amplitude of this curve represents the maximum speed of the object.
Q: What does the intersection of two lines on a velocity-time graph represent?
A:
The intersection of two lines on a velocity-time graph represents a point where two objects have the same velocity at the same time. This could mean they are at the same position if they're moving along the same path, but not necessarily if they're on different paths.
Q: How do you represent a car's journey with stops at traffic lights on a velocity-time graph?
A:
A car's journey with stops at traffic lights would be represented by a series of triangular or trapezoidal shapes on a velocity-time graph. Each shape would represent a period of acceleration (increasing velocity), constant speed (horizontal line), and deceleration (decreasing velocity). The stops would be shown as horizontal lines along the time axis where velocity is zero.
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