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Course: Mechanics (Essentials) - Class 11th > Unit 4
Lesson 7: Analyzing velocity time graphs- Velocity vs. time graphs
- Calculating average acceleration from graphs
- Calculating displacement from v-t graphs
- Finding displacement from velocity graphs
- Worked example: Area below v-t graph
- Area under a curved graph
- What are velocity vs. time graphs?
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Area under a curved graph
Let's explore how to calculate the area under a curved graph! Created by Vibhor Pandey.
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I don't get where was tf in the sigma notation :((1 vote)
t_f is the final time.
To find the area under a curved graph, i.e. sum of v across the interval t_i to t_f, we integrate v.
Let's take Worked example: Area below v-t graph as an example.A rabbit is trying to cross the road. Its velocity v as a function of time t is given in the graph, where rightwards is the positive velocity direction.
At what time does the rabbit have the same position as t = 0?
So now this problem is pretty easy.
2
∫ v dt = total distance in positive direction = p
0
t_f in this case is the final endpoint time.
x
∫ v dt = total distance in negative direction [2, x] = q
2
Now we just have to solve the equation for x.
p = q
If you are still unsure what am I doing, I strongly recommend you to check out AP Calculus AB or BC(1 vote)