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A particle moves along a straight line such that it's displacement x changes with time t as x=√at 2 +2bt+c where a,b and c are constants, then the acceleration varies as A) 1/x B)1/x 2 C)1/x 3 D)1/x 4

A particle moves along a straight line such that it's displacement x changes with time t as x=√at2+2bt+c where a,b and c are constants, then the acceleration varies as
A) 1/x
B)1/x2
C)1/x3
D)1/x4
 

Grade:11

1 Answers

Vikas TU
14149 Points
5 years ago
Acceleration is the double differentiation of displacement with respect to time.
.i.e. a = d2x/dt2
Therefore, dx/dt = 2√at + 2b = v (velocity)
Comparing from this the acceleration is  : 2√a
Substituting the value of t from velocity in displacement x we get,
x = √a((v – 2b)/2√a)^2 + 2b(v – 2b)/2√a + c
x = (v – 2b)/(2*2√a) +  2b(v – 2b)/2√a + c
or
x = ((v – 2b)/2+  2b(v – 2b))/2√a
Here 2√a is the acceleration and is inversely proportional to the x.
Hence, (A) option is correct.

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