Question

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

Answer 1

Step 1:Given:

$x=a+b{t}^2$

$a=8.5\text{m}$

$b=2.5\frac{\text{m}}{{\text{s}}^2}$

Step 2:Calculate distance at$t=2\text{s}$.

$$\begin{gathered} x_1=8.5+2.5\times {\left(2\right)}^2 \\ =8.5+10 \\ =18.5\text{m} \end{gathered}$$

Step 3:Calculate distance at $t=4\text{s}$.

$$\begin{gathered} x_2=8.5+2.5\times {\left(4\right)}^2 \\ =48.5\text{m} \end{gathered}$$

Step 4:Calculate the average velocity of the object.

$$\begin{gathered} v_{avg}=\frac{x_2-x_1}{t} \\ =\frac{48.5-18.5}{4-2} \\ =\frac{30}{2} \\ =15\frac{\text{m}}{\text{s}} \end{gathered}$$

Hence, the average velocity of the object is $15\frac{\text{m}}{\text{s}}$