In the one-dimensional motion of a particle, the relation between position x and time t is given by x2+2x=t (here x >0). Choose the correct statement :
The retardation of the particle is −14(x+1)3
The uniform acceleration of the particle is 1(x+1)3
The uniform velocity of the particle is 1(x+1)3
The particle has a variable acceleration of 4t+6.
A
The retardation of the particle is −14(x+1)3
B
The particle has a variable acceleration of 4t+6.
C
The uniform acceleration of the particle is 1(x+1)3
D
The uniform velocity of the particle is 1(x+1)3
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Solution
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x2+2x=t;x is distance and t is time
⇒2x.v+2v=1 ( Difference between t )
⇒v=1(x+1)2
⇒a=dxdt=−12(x+1)2×v
=−1(x+1)2×12(x+1)
⇒a=−14(x+1)3
The retardation of the particle is −14(x+1)3.
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