Question

☞︎︎︎ ᑭᕼYՏIᑕՏ ᑫᑌᗴՏTIOᑎ :-

➪ A ʙᴏᴅʏ ɪs ᴍᴏᴠɪɴɢ ᴜɴᴅɪʀᴇᴄᴛɪᴏɴᴀʟʟʏ ᴜɴᴅᴇʀ ᴛʜᴇ ɪɴғʟᴜᴇɴᴄᴇ ᴏғ ᴀ sᴏᴜʀᴄᴇ ᴏғ ᴄᴏɴsᴛᴀᴀɴᴛ ᴘᴏᴡᴇʀ. ɪᴛs ᴅɪsᴘʟᴀᴄᴇᴍᴇɴᴛ ɪɴ ᴛɪᴍᴇ ᴛ ɪs ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ ᴛᴏ -

a) $t^{ \frac{1}{2}}$

b) $t$

c) $t^{ \frac{3}{2}}$

d) $t^{2}$
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Answer 1

ANSWER:

• Displacement S is directly proportional to t^(3/2)

GIVEN:

• A body is moving unidirectionally under the influence of a source of constant power.

TO FIND:

• The displacement in time t.

EXPLANATION:

The body is moving unidirectionally under the influence of a source of constant power.

P = constant

$\boxed{ \bold{ \large{ \gray{P = F \times v }}}}$

$\boxed{ \bold{ \large{ \gray{F = ma }}}}$

P = ma × v

$\boxed{ \bold{ \large{ \gray{v = u + at }}}}$

u = 0

v = 0 + at

v = at

We know that P = ma × v

P = ma(at)

P = ma²t

$\sf {a}^{2} = \dfrac{P}{mt}$

$\sf a = \sqrt{ \dfrac{P}{mt}}$

$\boxed{ \bold{ \large{ \gray{S = ut + \dfrac{1}{2} a {t}^{2} }}}}$

u = 0

$\sf a = \sqrt{ \dfrac{P}{mt}}$

$\sf S = 0(t) + \dfrac{1}{2}\times \sqrt{ \dfrac{P}{mt}} \ {t}^{2}$

$\sf S = \dfrac{1}{2}\times \sqrt{ \dfrac{P}{m}} \ \dfrac{{t}^{2}}{{t}^{1\!/\!2} }$

$\sf S = \dfrac{1}{2}\times \sqrt{ \dfrac{P}{m}} \ {t}^{2 - 1\!/\!2}$

$\sf S = \dfrac{1}{2}\times \sqrt{ \dfrac{P}{m}} \ {t}^{3\!/\!2}$

$\sf S\ \propto \ {t}^{3\!/\!2}$

Hence displacement S is directly proportional to t^(3/2).