How to find acceleration at a Point on a GRAPH?

Question

i have a graph. Velocity on Y-axis, Time on x-axis. I have to find the acceleration at a few points on graph. How?

thanks

Answer 1

Acceleration is change in velocity / time.



On the graph mark a point at which we want to find acceleration.

P {x= a, y =b}. a gives the time and b gives the velocity at that instant of time.



On the x axis with a as center, mark two points left and right of ‘a’ such that the interval between the two points is one second.



In other words, mark on the x axis two points [a + 0.5] and [a – 0.5].



Time interval between the two points is now 1 s.



Next corresponding to the point [a + 0.5] find the velocity from the graph.

Similarly find the velocity corresponding to the point [a – 0.5].



The difference between the two values gives directly the acceleration at the point [a, b] since the time interval is one s.



Instead of taking time interval as one second, one can take still smaller value of time.



But in this case, we must divide the velocity difference by the time value.



Smaller the time value, greater is the accurate result for acceleration.



Repeat the procedure for other points also.

Answer 2

Acceleration On A Graph

Answer 3

Acceleration simply is the rate of change of velocity

means .:. a = v/t where a : acceleration , v :velocity, t : time



so all you need to do to get the acceleration @ any point on the graph is to take it's velocity value on y-Axis( by drawing a perpendicular line from the point to Y-Axis ) & divide it by it's corresponding time value on x-axis( by drawing a perpendicular line from the point to X-Axis )



i hope this helpful

Answer 4

We know a method of graphical derivation at a given point of your graph. It leads to a tangent to the graph. The slop of that line, if the units on the axes are well chosen gives you the acceleration for which you are looking for.

Answer 5

This is an interesting idea.

The slope of the velocity vs. time graph is acceleration vs. time. The slope of the displacement vs. time graph is velocity vs. time. But, the more interesting part is that the area underneath the acceleration vs. time is the velocity vs. time. And the area underneath the velocity vs. time is the displacement vs. time.

This is explained in calculus, simply by derivatives and integrals, but just play around with it, and see how it makes sense.

Answer 6

Find the gradient of that point....this can be done by drawing a tangential line to the point as best as possible and finding the gradient of it....