Acceleration Time Graph: Learn with Vedantu
The acceleration time graph is the graph that is used to determine the change in velocity in the given interval of the time. In the acceleration vs time graph on the x-axis you have the time taken by the object and on the y-axis acceleration of the object, in which the area under the graph gives you the change in velocity of the object over the given period of the time. The acceleration time graph is used to find the change in the velocity of the moving object for the given period of time and this can be determined by finding the area under the curve.
Understanding The Acceleration Time Graph
To understand the graph of the acceleration vs time graph you must have an idea about some terminologies. Let us discuss these terminologies first.
Acceleration:- It is the ratio of the change in velocity in the given time interval. The SI unit of the acceleration is m2/sec. In simple words acceleration means to gain and lose the velocity of the vehicle.
Velocity:- The velocity of an object is defined as the ratio of the change in the position of the object in the given time interval. The SI unit of velocity is m/sec.
Time period:- The time period is defined as the interval of the time given to perform the specific activity.
Area Under The Acceleration Time Graph
The area under the graph gives the change in the velocity of the object in the given interval of the time. This means the area under the curve of the acceleration time graph is equal to the change in the velocity of the object in the given time period.
The area under curve = â–³v
You can represent the change in velocity as â–³v, change in acceleration as â–³a and change in time as â–³t
According to the definition of the acceleration,
â–³a = â–³v/â–³t
By multiplying the â–³t that is change in time interval to both sides, we get,
â–³a = â–³v/â–³t
This is the direct theoretical formula which can be used to find any of the three values for which the other two are given. What if there is only a graph given in the place of the data? In that case, you will figure out the shapes formed under the graph and find the area of that figure according to the parameters required to calculate that.
Let us consider some examples to understand the topic more precisely.
Examples Of Acceleration Time Graph
Example:- The initial velocity of an object is 6m/sec, the change in the acceleration of the object in 10 seconds is 2m2/sec. Find the final velocity of the object?
Answer:- As there is the direct data given in the question so here solve the question by the formula that we have,
â–³v = â–³aâ–³t
â–³a that is a change in acceleration = 2m2/sec, â–³t which is symboled for the time interval
= 10 sec so by the formula we get the change in velocity as,
â–³v = â–³aâ–³t
â–³v = 2 x 10
â–³v = 20 m/sec
â–³v is the change in velocity which means that the difference between the final velocity and initial velocity of the object.
â–³v = vf - vi
20 = vf - 6 ( initial velocity is given in the question as 6 m/sec)
vf = 26 m/sec
The final velocity of the object is 26 m/sec.
Example:- There is an acceleration vs time graph given, then find the initial velocity of the object if the final velocity of the object was 40m/sec.
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Answer:- As there is a graph that has the figure under the curve so you have to find the area under the acceleration time graph.
As you can see clearly, the graph has three figures, two triangles and one rectangle. So you need to find the area of these figures to find the change in the velocity of the object.
â–³v = area of rectangle + area of â–³1+ area of â–³2
△v = LB+ ½ base.height+½ base.height (data as per the given graph)
△v = 3x4 + ½ x 4x 4 + ½ x 2 x 2
â–³v = 12 + 8 + 2
â–³v = 22 m/sec
â–³v is the change in velocity which means that the difference between the final velocity and initial velocity of the object.
â–³v = vf - vi
22 = 40 - vi ( final velocity of the object 40 m/sec given in the question)
vi = 40-22
vi = 18m/sec
The final velocity of the object is 18m/sec.
Important Things To Remember In Acceleration Time Graph
Acceleration Time Graphs are very easy to understand and the questions based on this topic are often easily solvable in a small amount of time during the examination. This makes Acceleration Time Graphs a very scoring topic in the examination and it is often solved by everyone. But at the same time, students can make small mistakes that can generate wrong answers. However, Vedantu has covered this with some important points to remember for students while solving Acceleration Time Graphs.
The slope of Acceleration Time Graphs gives you the value of jerk. Jerk refers to a sudden motion for a short period of time in which acceleration generally experiences sudden change. In technical terms, jerk is defined as the rate of change of acceleration of the moving or stationary body with respect to time. One of the examples of jerky motion can be when one drives over a speed breaker without applying brakes. The passengers in the vehicle will experience sudden motion and this motion is called jerky motion. When one applies brakes suddenly, the passenger will again jerky motion because the vehicle has suddenly decelerated.
The area of Acceleration Time Graphs will yield the change of the velocity of the system. The complete area under the curve will give you the change of the velocity of the system in the complete journey. However, one can also find the rate of change of velocity between two points by selecting those two points and drawing the vertical line from those points to the x axis which represents the change in time. This will result in a shape that is generally a quadrilateral or triangle in the examinations. Students should be very careful when selecting the points and calculating the values to ensure one reaches the correct answer.
- Students should be very careful with the units that are given in the Acceleration Time Graphs and the question. It is very important to note that in order to put the values in the appropriate formula, all the quantities should have correct units. Failing to do so may lead to a wrong answer. Unit of time is seconds, minutes or hours, units of acceleration are m/ sec 2 or km/ hr 2 and the units of velocity are m/ sec or km/ sec. Students should note them down and remember as this will be very useful when solving any questions from the Acceleration Time Graphs topic.
FAQs on Acceleration Time Graph
1. How can you find the area under the acceleration time graph having an uneven curve?
The area under the acceleration time graph is the sum of the small rectangles which can be formed under any kind of curve. It is obvious that the area of a rectangle and a curve will give you the different answers but when you divide that curve into the smallest rectangle which gives you the negligible difference in the area that would not make any considerable change in the answer. And to find the area under the curve, break that curve into those figures whose area is easy to find.
2. Can we find the velocity of the object at a particular point of time with the help of an acceleration time graph?
No. One cannot calculate the velocity of the object directly from the graph at a particular time. However, there is another way to find it. We can only find the change in velocity by the area under the acceleration time graph by calculating the area under the curve to the given time. Then by the formula of the difference in the final and initial velocity you can find the final velocity of the object in the given time period. Hence, we can say we can determine the velocity of the particle between certain instances.
3. What do you mean by the area under the curve?
The area under the curve signifies the area occupied by the curve and the vertical axis or the X-axis. To find the area under the curve between two specific points, draw a line parallel to the Y-axis from those two points till it reaches the X-axis. The significance of the area under the curve in the Acceleration time graph is that we can obtain the velocity with this. As the area under this curve will have acceleration and time components multiplied with each other, it gives rise to the velocity between those two points.
4. I find the questions related to the Acceleration time graph wherein the motion is represented by a graph. How can I improve myself while dealing with such questions?
The questions related to the acceleration time graph may look lengthy and difficult because of the graph. But this is not true. In fact, the graph-based questions are one the easiest ones to solve as the graph provides all the information one needs to solve and approach these questions. Because of this, it's very easy to find the required answer. Once students understand the concepts and solve questions based on these topics, they will solve these questions easily in exams. Concepts related to this are given in Vedantu.
5. What is the importance of learning Acceleration Time Graph and how will Vedantu help students?
Acceleration and time graphs are important as they give complete information about the acceleration of the particle in a specific period of time. This helps us to understand whether the particle is accelerating or decelerating based just by looking at the graph. It is also easy to find the velocity of the particle at a distance between a certain instance as it can be obtained by finding the area under the curve. Vedantu has all the concepts related to the Acceleration Time graph along with important formulas and examples. Students should take advantage of this important study material.
