Question

The position of the particle moving on $X$-axis is given by, $X=A{t}^3+B{t}^2+Ct+D.$ The numerical values of $A,B,C,D$ are $1,4,-2$ and $5$ respectively and SI units are used. Find the average velocity during the interval $t=0$ to $t=4s$.

• A. $25\frac{m}{s}$
• B. $35\frac{m}{s}$
• C. $40\frac{m}{s}$
• D. $30\frac{m}{s}$

Answer 1

The correct option is D $30\frac{m}{s}$

$X=A{t}^3+B{t}^2+Ct+D$
Position at $t=0$ is $X=D=5m$
Position at $t=4s$ is $(1\times 4^3+4\times 4^2-2\times 4+5)m=125m$
Thus, the displacement during $0$ to $4s$ is $(125-5)m=120m$
$\therefore$ Average velocity, $v_{av}=\frac{Displacement}{time}=\frac{120}{4}=30\frac{m}{s}$