Question

# The position of a particle moving along the $$x-$$ axis is expressed as $$x={at}^{3}+{bt}^{2}+ct+d$$. The initial acceleration of the particle is

A
6a
B
2b
C
a+b
D
a+c

Solution

## The correct option is B $$2b$$The relationship between position and time is given by the equation,$$x=at^3+bt^2+ct+d$$Velocity, $$v=\dfrac{dx}{dt}$$$$v=3at^2+2bt+c$$Acceleration, $$a=\dfrac{dv}{dt}$$$$a=6at+2b$$The initial acceleration at time $$t=0sec$$$$a|_{t=0sec}=6a(0)+2b$$$$a|_{t=0sec}=2b$$The correct option is B.Physics

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