Question

drive equation second and third of motion by velocity time graph

Answer 1

3. Derive v2 = u2 + 2as by Graphical MethodVelocity–Time graph to derive the equations of motion.We have just seen that the distance travelled s by a body in time t is given by the area of the figure OABC which is a trapezium. In other words,Distance travelled, s=Area of trapezium OABCNow, OA + CB = u + v and OC = t. Putting these values in the above relation, we get: ...... (7)We now want to eliminate t from the above equation. This can be done by obtaining the value of t from the first equation of motion. Thus, v = u + at (First equation of motion)
And, at = v – u or Now, putting this value of t in equation (7) above, we get: or 2as=v2 – u2 [because (v + u) × (v – u) = v2 – u2]or v2=u2 + 2asThis is the third equation of motion.erive s = ut + (1/2) at2 by Graphical MethodVelocity–Time graph to derive the equations of motion.Suppose the body travels a distance s in time t. In the above Figure, the distance travelled by the body is given by the area of the space between the velocity – time graph AB and the time axis OC,which is equal to the area of the figure OABC. Thus:Distance travelled=Area of figure OABC=Area of rectangle OADC + Area of triangle ABDWe will now find out the area of the rectangle OADC and the area of the triangle ABD.(i) Area of rectangle OADC=OA × OC=u × t=ut ...... (5)(ii) Area of triangle ABD=(1/2) × Area of rectangle AEBD=(1/2) × AD × BD=(1/2) × t × at (because AD = t and BD = at)=(1/2) at2...... (6)So, Distance travelled, s=Area of rectangle OADC + Area of triangle ABDor s = ut + (1/2) at2
This is the second equation of motion. It has been derived here by the graphical method.


i am sorry for not giving the figure. i cant upload the image. i think you will be having it in your text

Answer 2

■HEY DEAR

●SECOND EQUATION OF MOTION

Distance = Area of rectangle + Area of triangle.

(I) Area of rectangle = OA×OC

. = u × t =ut

(ii) Area of triangle = 1/2 × AD × BC

. =1/2 × t × at

Now ,putting this value in formula.

S= ut + 1/2 at^2 .

●THIRD EQUATION OF MOTION

DISTANCE Travelled =Area of Trapezium = 1/2 × sum of the parallel side × height.

S=》1/2 ×( OA + BD) x OC

S=》1/2 × u+v×t

Now, to estimate "t"

t= v-u / a

NOW, putting this value of "t" in equation .

S = (U+V) × (V-U) 《= [a^2-b^2]

2a

2as = v^2 - u^2

v^2 = u^2+2as.

■HOPE ITS HELPFULL

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