Question

38. Show by means of graphical method that:
V = u + at
where the symbols have their usual meanings.
39. Show by using the graphical method that:
S=ut + 1/2at^2
where the symbols have their usual meanings.
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Answer 1

Answer:

38. Show by means of graphical method that:

V = u + at

where the symbols have their usual meanings.

39. Show by using the graphical method that:

S=ut + 1/2at^2

where the symbols have their usual meanings.

Explanation:

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Answer 2

Answer:

Velocity–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 ABD

We 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 ABD

or s = ut + (1/2) at2

This is the second equation of motion. It has been derived here by the graphical method.

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