Kinematics 5 Question 4

6. The position of a particle as a function of time t, is given by x(t)=at+bt2ct3 where a,b and c are constants. When the particle attains zero acceleration, then its velocity will be

(2019 Main, 09 April II)

(a) a+b22c

(b) a+b24c

(c) a+b23c

(d) a+b2c

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Answer:

Correct Answer: 6. (c)

Solution:

  1. Position of particle is, x(t)=at+bt2ct3

So, its velocity is, v=dxdt=a+2bt3ct2

and acceleration is, a=dvdt=2b6ct

Acceleration is zero, then 2b6ct=0

t=2b6c=b3c

Substituting this ’ t ’ in expression of velocity, we get

v=a+2b(b3c)3c(b3c)2=a+2b23cb23c=a+b23c



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