Question

Q13. Derive equation with diagram
á. Position - time relation
b. Position - velocity relation​

Answer 1

Answer:

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A. Position - time relation

Distance covered by the object in the given time t is given by the area of the trapezium ABDOE

Let in the given time, t the displacement covered by the moving object = s

The area of trapezium, ABDOE

Displacement (s) = Area of ABD + Area of ADOE

= 21​×AB×AD+AE×OE, AB=DC=at

= 21​at×t+ut

Hence

s=ut+21​at2     (2nd equation of motion)

Explanation:

B.  Equation for position velocity relation....consider graph given  in figure .

We know that distance travelled s by a body in time t is given by the area under line AB which is area of trapezium OABC.

So we have

Distance travelled=s= Area of Trapezium OABC

S=(sum of parallel sides) x height/2

=(OA+CB)x OC/2

since OA+CB=u+v and OC=t,

Then we gt

s=(u+v)t/2get,-------------(1)

from, velocity time relation,

t=v-u/a

substituting the value of 't' in equation 1

we get,

s=(u+v)/2(v-u)/2

or we have

v²=u²+2as

which is equation for position velocity relation