A truck travels due east for a distance of $1.6 \mathrm{~km}$, turns around and goes due west for $7.5 \mathrm{~km}$, and finally turns around again and travel
(a) What is the total distance (in km) that the truck travels? (Enter a number.)
The question asks for the total distance traveled, regardless of direction. $\mathrm{km}$
(b) What are the magnitude (in $\mathrm{km}$ ) and direction of the truck's displacement? (Enter a number.) magnitude
Displacement is the change in position, that is, the difference between the initial and final position. km direction
east
west
neither
Answer
\(\boxed{\text{The total distance that the truck travels is 9.1 km. The magnitude of the truck's displacement is 5.9 km in the west direction.}}\)
Step 1 ：The truck travels due east for a distance of \(1.6 \mathrm{~km}\), turns around and goes due west for \(7.5 \mathrm{~km}\).
Step 2 ：The total distance traveled by the truck is the sum of all the distances it covered in each direction. This can be calculated as \(1.6 \mathrm{~km} + 7.5 \mathrm{~km} = 9.1 \mathrm{~km}\).
Step 3 ：Displacement is the change in position, that is, the difference between the initial and final position. Since the truck initially traveled east, then west (which is the opposite direction), its displacement would be the total distance it traveled west minus the distance it traveled east. This can be calculated as \(7.5 \mathrm{~km} - 1.6 \mathrm{~km} = 5.9 \mathrm{~km}\).
Step 4 ：\(\boxed{\text{The total distance that the truck travels is 9.1 km. The magnitude of the truck's displacement is 5.9 km in the west direction.}}\)
