Worksheet: Position, Displacement, and Distance
In this worksheet, we will practice differentiating between position, displacement, and distance involving using vector notation.
What kind of information does this signpost show?
What is the name of the vector quantity which gives the total change of a particle’s position?
- Bacceleration vector
- Dvelocity vector
If the position vector of a body at time is given by , find its displacement .
A particle moving in a straight line has a position vector , defined by the relation , where is the time, measured in seconds, and is a unit vector. Determine the magnitude of the displacement vector in meters after 4 seconds.
The position vector of a particle relative to the point is given by the relation , where is a fixed unit vector and is the time. Find the displacement of the particle after 3 seconds.
A person ran 160 m east and then 175 m north. Find the total distance covered by the person.
A person rode a bicycle 7 km west and then 13 km north of west. Find the total distance covered by the person.
A car moved east and then north. Find the magnitude and direction of its displacement, rounding the angle to the nearest minute.
- A meters, north of east
- B meters, north of west
- C375 meters, north of east
- D meters, south of east
- E meters, north of east
According to the figure, a body moved from to along the line segment , and then it moved to along . Finally, it moved to along and stopped there. Find the distance covered by the body and the magnitude of its displacement .
Given that a ship covered 300 m due west and then 675 m due north, determine its displacement, approximating its angle to the nearest minute.
- A975 m, south of east
- B m, north of west
- C m, north of west
- D450 m, north of east
A bird leaves its nest and flies for 5 kilometers in the direction north of east before stopping to rest in a tree. It then flies 10 kilometers southeast from the tree, landing on top of a telephone pole. Given that the vector represents a displacement of 1 kilometer east and the vector represents a displacement of 1 kilometer north, find the vector that represents the displacement of the telephone pole from the nest.
A man walks from his house to a bank and then from the bank to a supermarket. Given that the displacement of the bank from his house is represented by the vector and the displacement of the supermarket from the bank is represented by the vector , what does the vector represent?
- Athe displacement of the supermarket from the bank
- Bthe displacement of the bank from the supermarket
- Cthe total distance the man traveled to the supermarket
- Dthe displacement of the man’s house from the supermarket
- Ethe displacement of the supermarket from the man’s house
You traveled 213 miles from California to San Francisco. Does the “213 miles” represent distance or displacement?
If you were lost in a forest, would you prefer to know your distance or your displacement from the nearest settlement?
The displacement of a particle of unit mass is given as a function of time by the relation , where is constant unit vector, measured in centimeters , and in seconds. Given that the particle started its motion at , find the total distance covered in the first 5 seconds of its motion.
Mason and Amelia started walking from the same point. Mason walked 1 mile southwest and then 3 miles northwest. Amelia walked 3 miles northwest and then 1 mile southwest. What can you say about where they ended up?
- AThey ended up 2 miles apart.
- BThey ended up at the same place.
- CThey ended up 4 miles apart.
- DMason is west of Amelia.
- EThey ended up 6 miles apart.
A particle started moving along a straight line. At time (where ), its position relative to a fixed point is given by Determine all the possible value of at which .