How to Read and Interpret a Velocity Time Graph
The velocity of a moving object is defined as the rate of change of displacement of the moving object. Therefore, velocity is a vector quantity and its variation with time in graphical terms is known as the velocity-time graph or velocity-time relation. The sprinter's changing speed, as well as the speed of any other moving object or person, is displayed on a velocity-time graph. The slope of the graph line on a velocity-time graph is used to illustrate acceleration.
Velocity-Time Graph for Uniform Motion (No Acceleration)
In this case, the velocity of a moving object is constant and does not change with time, since there is no acceleration applied on the object. Therefore, for this case, one can see (as shown below in Figure (a)) that the velocity will remain constant during the whole trip despite the change in the time.
Velocity-Time Graph with a Constant Uniform Acceleration
In this case, the object is under a constant uniform acceleration, and therefore, its velocity will constantly increase or decrease depending on the applied uniform application, which is called the accelerating and retarding acceleration, respectively. In the velocity-time graph (as shown below in Figure (b)), the velocity of the object increases linearly on the application of constant uniform acceleration, and therefore, we observe a linear behaviour of the object’s velocity with time. The slope of this graph can be utilised to estimate the acceleration applied on the object.
Under a uniform constant acceleration, the equations of motion of the object can be expressed as follows:
\[v = u + at - - - - - (1)\]
\[S = ut + \dfrac{1}{2}a{t^2} - - - - - (2)\]
\[{v^2} = {u^2} - 2as - - - - - (3)\]
where u, v, a, s and t are the initial velocity, final velocity, uniform acceleration, total displacement of the object and travel/trip time, respectively.
Velocity Time Graph for (a) Constant Uniform Velocity, (b) Constant Uniform Acceleration, and (c) Under a Variable Acceleration.
Velocity-Time Graph Under a Variable Acceleration
In this case, the acceleration acting on the object changes with the time, and therefore, the variation in the velocity of the object is different in the different time periods of the trip (as shown in FIgure (c) above), and therefore, we observe a velocity-time graph different from the case where the uniform acceleration is applied on the object, and we observe a parabolic behaviour of velocity with time.
Interesting Facts
Speed is a scalar quantity and velocity is a vector quantity.
The fastest speed possible is the speed of light.
In the uniform circular motion, the speed of the object remains constant while the velocity of the object varies continuously.
Key Features
Velocity is the rate of change of the displacement.
In the velocity-time graphs, the slope of the curves manifests the acceleration of the object.
The velocity of any object is based on the rate of change of displacement and therefore depends on the initial and final position of the object.
FAQs on Velocity Time Graph Explained for Students
1. What is a velocity-time graph and what does it fundamentally represent?
A velocity-time graph is a powerful tool in physics that visually represents an object's motion. It plots the velocity of an object on the vertical (y-axis) against time on the horizontal (x-axis). Fundamentally, this graph shows how an object's velocity changes over a specific period, allowing for a detailed analysis of its acceleration and displacement.
2. What key information can be determined from the slope of a velocity-time graph?
The slope (or gradient) of a velocity-time graph represents the object's acceleration. This is because acceleration is defined as the rate of change of velocity. There are three primary scenarios:
- A positive slope (line goes up) indicates positive acceleration, meaning the object is speeding up.
- A negative slope (line goes down) indicates negative acceleration (retardation or deceleration), meaning the object is slowing down.
- A zero slope (a flat horizontal line) indicates zero acceleration, meaning the object is moving at a constant velocity.
3. How is an object's displacement calculated using a velocity-time graph?
The displacement of an object is calculated by finding the area under the line of a velocity-time graph. The area between the graph line and the time axis (x-axis) gives the total change in position. For simple motions, this area can be calculated using standard geometric formulas for rectangles (for constant velocity) or triangles (for constant acceleration from rest).
4. What is the difference between a velocity-time graph for uniform motion and one for uniformly accelerated motion?
The key difference lies in the shape of the line. For uniform motion (constant velocity), the graph is a flat horizontal line, indicating that the velocity does not change over time (zero acceleration). For uniformly accelerated motion, the graph is a straight, sloped line. The constant slope shows that the velocity is changing at a steady rate.
5. Can the line on a velocity-time graph go below the x-axis? What does this signify?
Yes, the line on a velocity-time graph can go below the x-axis. This is a crucial concept that signifies the object is moving with a negative velocity. In physics, this means the object is moving in the opposite direction from the one designated as positive. For example, if moving to the right is positive, a graph line below the x-axis represents movement to the left.
6. Why would a velocity-time graph be a curved line instead of a straight one?
A velocity-time graph is a curved line when the object is undergoing non-uniform acceleration. This means its acceleration is not constant but is changing over time. In such a case, the slope of the line is continuously changing. To find the acceleration at a specific moment, one must calculate the slope of the tangent to the curve at that point in time.
7. How does a velocity-time graph fundamentally differ from a speed-time graph?
The fundamental difference lies in the quantities they represent:
- Velocity is a vector: A velocity-time graph can have negative values (below the x-axis) to show motion in the opposite direction. The area under this graph gives displacement.
- Speed is a scalar: A speed-time graph can never have negative values, as speed cannot be negative. The line will always be on or above the x-axis. The area under this graph gives the total distance travelled.
