Question

The position of an object moving along $x$-axis is given by $x = a + bt^2$, where $a = 8.5\, m$ and $b = 2.5\, m\, s^{-2}$ and $t$ is measured in seconds. The average velocity of the object between $t = 2 \,s$ and $t = 4\, s$ is

• A. $5\,m\,s^{-1}$
• B. $10\,m\,s^{-1}$
• C. $15\,m\,s^{-1}$
• D. $20\,m\,s^{-1}$

Answer 1

Answer: (C)

Average velocity, $\bar{v}=\frac{\left(x\right)_{t=4}-\left(x\right)_{t=2}}{4-2}$
$\bar{v}=\frac{\left(a+b\left(4\right)^{2}\right)-\left(a+b\left(2\right)^{2}\right)}{4-2}$
$=\frac{\left(a+16b\right)-\left(a+4b\right)}{4-2}=6b$
$=6\left(2.5\right)m\,s^{-1}=15\,m\,s^{-1}$