The Solution:
Given that the distance is defined by the function below:
[tex]d(t)=t^3-2t+2[/tex]
We are required to find the average speed of the ladybug from t=1 second to t=3 seconds in inches/second.
Step 1:
For t=1 second, the distance in inches is
[tex]d(1)=1^3-2(1)+2=1-2+2=1\text{ inch}[/tex]
For t=3 seconds, the distance in inches is
[tex]d(3)=3^3-2(3)+2=27-6+2=21+2=23\text{ inches}[/tex]
By formula,
[tex]\text{ Average Speed=}\frac{\text{ distance covered}}{\text{ time taken}}[/tex]
In this case,
Distance covered = change in distance, which is
[tex]\text{ change in distance=d(3)-d(1)=23-1=22 inches}[/tex]
Time taken = change in time, which is:
[tex]\text{ Change in time=t}_2-t_1=3-1=2\text{ seconds}[/tex]
Substituting these values in the formula, we get
[tex]\text{ Average Speed=}\frac{22}{2}=11\text{ inches/second}[/tex]
Therefore, the correct answer is 11 inches/second.
