Question

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

• A. $10\text{m/s}$
• B. $15\text{m/s}$
• C. $12\text{m/s}$
• D. $7.5\text{m/s}$

Answer 1

The correct option is B $15\text{m/s}$

Average velocity $=\frac{\text{Displacement}}{\text{Time taken}}$
At $t=2\text{s},x_1=a+4b$
At $t=4\text{s},x_2=a+16b$
$Displacement=x_2-x_1=12b$
$=12\left(2.5\right)=30m$
Average velocity =$\frac{\text{30m}}{\text{2s}}$ =15${\text{ms}}^{-1}$