Question

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

• A. $b,-4d$
• B. $-b,2c$
• C. $b,2c$
• D. $2c,-4d$

Answer 1

Answer: (C)

$b,2c$

Velocity $=v=\frac{dy}{dt}=b+2ct-4d{t}^3$

$v_0=b+2c\left(0\right)-4d{\left(0\right)}^3=b$ (for initial velocity, $t=0$)

And acceleration $=a=\frac{dv}{dt}=2c-12d{t}^2$

$\therefore$ Initial acceleration =$a_0=2c-12d{\left(0\right)}^2=2c$