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

Question

The displacement of a particle is given by y=a+b t+c t2-d t4 The initial velocity and acceleration are respectively (A) b,-4 d (B) -b, 2 c (C) b, 2 c (D) 2 c,-4 d

Tardigrade Admin · Accepted Answer

v=(d y/d t)=b+2 c t-4 d t3 v0= b +2 c(0)-4 d(0)3=b (∵ for initial velocity, t=0) Now a=(d v/d t)=2 c-12 d2 ∴ a0=2 c-12 d(0)2=2 c,( text at t=0)

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

$b, - 4 d$

$- b, 2 c$

$b, 2 c$

$2 c, - 4 d$

$v = \frac{d y}{d t} = b + 2 c t - 4 d t^{3}$
$v_{0} = b + 2 c (0) - 4 d (0)^{3} = b$
$(∵$ for initial velocity, $t = 0)$
Now $a = \frac{d v}{d t} = 2 c - 12 d^{2}$
$∴ a_{0} = 2 c - 12 d (0)^{2} = 2 c, (at t = 0)$

Q. The displacement of a particle is given by y=a+bt+ct2−dt4 The initial velocity and acceleration are respectively

b,−4d

−b,2c

b,2c

2c,−4d