Derive equation v^{2}-u^{2}=2 a S graphically.

English

Gujarati

Hindi

7. MOTION

hard

Derive the equation $v^{2}-u^{2}=2 a S$ graphically.

Option A

Option B

Option C

Option D

Solution

Consider the figure given below

Now, area of trapezium $OABD$

$=\frac{( OA + BD ) \times OD }{2}$

Now, $OA =u, BD =v,$ and $OD =t$

Therefore, we have

$S =\frac{(u+v) t}{2}$

or $S=\frac{(u+v)(v-u)}{2 a},$ using $v=u+a t$

Hence, we have

$v^{2}-u^{2}=2 a S$

Standard 9

Science

Share

Similar Questions

Define distance and displacement. A body covers one complete revolution around a circular park of circumference $176 \,m$ in $4$ minutes. Find the displacement of the body after $6$ minutes.

medium

The velocity$-$time graph of a truck is plotted below

$(a)$ Calculate the magnitude of displacement of the truck in $15$ seconds.

$(b)$ During which part of the journey was the truck decelerating ?

$(c)$ Calculate the magnitude of average velocity of the truck.

medium

Give one similarity and one dissimilarity between the two graphs

medium

A moving body is covering a distance directly proportional to the square of time. The acceleration of the body is

easy

Explain the following type of motion with one example of each

$(i)$ Acceleration is positive

$(ii)$ Acceleration is negative

$(iii)$ Acceleration is zero.

medium