Question

Derive the equation for position - time relation (S=ut+1/2 at² ) by graphs method

Answer 1

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As per the second equation of motion, we know that,

S = ut + 1/2 at²

According to the graph

Distance = area under v-t graph

Distance = area of OABD

Distance=area of OABD rectangle+area of ∆ ABC

.°. S = OA × OD + 1/2 × AC × BC

S = u × t + 1/2 × t × (v–u)............ ➊

From first equation of motion

V = u + at

v – u = at

Now, putting v–u = at in equation ➊

S = ut + 1/2 × t × (at)

.°. S = ut + 1/2 at²

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Answer 2

Answer:

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As per the second equation of motion, we know that,

S = ut + 1/2 at²

According to the graph

Distance = area under v-t graph

Distance = area of OABD

Distance=area of OABD rectangle+area of ∆ ABC

.°. S = OA × OD + 1/2 × AC × BC

S = u × t + 1/2 × t × (v–u)............ ➊

From first equation of motion

V = u + at

v – u = at

Now, putting v–u = at in equation ➊

S = ut + 1/2 × t × (at)

.°. S = ut + 1/2 at²

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