Question

A particle starts from rest and moves along a straight line with constant acceleration. The variation of velocity v with displacement S is : ( Please give full explanation)

Answer 1

Explanation:

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Answer 2

Answer:

The variation of velocity v with displacement S is $\frac{vt}{2} =s$

Explanation:

we know that acceleration is the rate of chnage of velocity

$a=\frac{dv}{dt}$........................(1)

as per the question acceleration is constant so,

$cdt=dv$...............(2)    where c=constant

integrate (2) both sides

$\int\ {c} \, dt=\int\ {} \, dv$

so,

$ct=v$...........................(3)

and we also know that velocity is defined as rate of change of displacement

$v=\frac{ds}{dt}$

after rearranging we get

$vdt=ds$.......................(4)

put $v=ct$ in (4)

we get

$ctdt=ds$

integrating both sides we get

$\int\ {ct} \, dt=\int\ {} \, ds$

after solving we get

$\frac{ct^2}{2} =s$

$\frac{ct\times t}{2} =s$..........................(5)

from (3) and (5)

$\frac{vt}{2} =s$

The variation of velocity v with displacement S is $\frac{vt}{2} =s$