Question

Question 6.10 A body is moving unidirectionally under the influence of a source of constant power. Its displacement in time t is proportional to

(i) t^(1/2)
(ii) t
(iii) t^(3/2)
(iv) t^2

Chapter Work, Energy And Power Page 136

Answer 1

A/C to question ,
A body is moving unidirectional under the influence of a source of constant power . Let P is the power .
e.g P = constant
but we know,
Power = Force × velocity
e.g P = F× V
P = ma × V [ F = ma ]

we know,
V = U + at
when, U = 0 [ Let body starts to move initially at rest ]
V = 0 + at
V = at use this in above equation
P = ma × at
P = ma²t
a = √{P/mt} ___________(1)

again , use motion equation ,
S = Ut + 1/2at²
S is displacement so, Let x
x = 0.t + 1/2× √{P/mt}× t²
x = √{P/m} × t³/t½
x = √{P/m} × t^(3/2)
hence , x is directly proportional to t^(3/2)
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Answer 2

Answer: option (c) is correct

Explanation is given below