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  4. The displacement of a particle is given by y=a+b t+c t2-d t4 The initial velocity and acceleration are respectively

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Q. The displacement of a particle is given by
$y=a+b t+c t^2-d t^4$
The initial velocity and acceleration are respectively

Motion in a Straight Line

Solution:

$v=\frac{d y}{d t}=b+2 c t-4 d t^3$
$v_0= b +2 c(0)-4 d(0)^3=b $
$(\because$ for initial velocity, $t=0)$
Now $a=\frac{d v}{d t}=2 c-12 d^2$
$\therefore a_0=2 c-12 d(0)^2=2 c,(\text { at } t=0)$