Question

what is v-t graph ? show that v²=vo²+2ax where the symbols have their unsual meaning​

Answer 1

The body has an initial velocity u at a point A and then its velocity changes at a uniform rate from A to B in time t. In other words, there is a uniform acceleration a from A to B, and after time t its final velocity becomes v which is equal to BC in the graph. The time t is represented by OC. 

To complete the figure, we draw the perpendicular CB from point C, and draw AD parallel to OC. BE is the perpendicular from point B to OE. 

Now, Initial velocity of the body, u=OA                         ...(1) 

And, Final velocity of the body, v=BC                              ...(2) 

But from the graph BC=BD+DC

Therefore, v=BD+DC                                                 ...(3) 

Again DC=OA

So, v=BD+OA

Now, from equation (1), OA=u

So, v=BD+u                                                          ...(4) 

We should find out the value of BD now. We know the slope of a velocity-time graph is equal to the acceleration, a. 

Thus, Acceleration, a= slope of line AB

or a=ADBD

But AD=OC=t, so putting t in place of AD in the above relation, we get: 

a=tBD

or BD=at

Now, putting this value of BD in equation(4), we get: 

v=u+at

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Answer 2

Velocity Time graph.

A velocity-time graph shows the speed and direction an object travels over a specific period of time. Velocity-time graphs are also called speed-time graphs.

The vertical axis of a velocity-time graph is the velocity of the object. The horizontal axis is the time from the start.

For 2nd question, refer the attachement.

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