Motion in a Straight Line - Result Question 10

10. A particle of unit mass undergoes onedimensional motion such that its velocity varies according to v(x)=bx2n

where b and n are constants and x is the position of the particle. The acceleration of the particle as the function of x, is given by:

(a) 2nb2x4n1

(b) 2b2x2n+1

(c) 2nb2e4n+1

(d) 2nb2x2n1

[2015]

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Answer:

Correct Answer: 10. (a)

Solution:

  1. (a) Given, v(x)=bx2n

a=dvdt=dvdxdxdt

=vdvdx

So, dvdx=2nbx2n1

Acceleration of the particle as function of x,

a=vdvdx=bx2nb(2n)x2n1=2nb2x4n1

For one dimensional motin, the angle between velocity and acceleration is either 0 or 180 and it does not change with time.



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