Question

The displacement of a particle moving in a straight line is given by the expression $x=A t^{3}+B t^{2}+C t+D$ in metres, where $t$ is in seconds and $A, B, C$ and $D$ are constants. The ratio between the initial acceleration and initial velocity is

• A. $\frac{2 C}{B}$
• B. $\frac{2 B}{C}$
• C. $2 \bar{C}$
• D. $\frac{C}{2 B}$

Answer 1

Answer: (B)

Displacement of a particle moving in a straight
$\operatorname{line}(x)=A t^{3}+B t^{2}+C t+D$
$\therefore \text { Velocity, } v=\frac{d x}{d t}=3 A t^{2}+2 B t+C$
$V_{\text {initial }}=C $
and $a=\frac{d^{2} x}{d t^{2}}=6 A t+2 B$
$a_{\text {initial }}=2 B$
$\therefore $ Ratio between initial acceleration and initial velocity is $\frac{2 B}{C}$