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Question

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 :
  1. The retardation of the particle is 14(x+1)3
  2. The uniform acceleration of the particle is 1(x+1)3
  3. The uniform velocity of the particle is 1(x+1)3
  4. 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
Solution
Verified by Toppr

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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