# Worksheet: Position, Displacement, and Distance

In this worksheet, we will practice differentiating between position, displacement, and distance involving using vector notation.

**Q2: **

What kind of information does this signpost show?

- Adistance
- Bvelocity
- Cdisplacement
- Dspeed

**Q3: **

What is the name of the vector quantity which gives the total change of a particleβs position?

- Adistance
- Bacceleration vector
- Cdisplacement
- Dvelocity vector

**Q4: **

If the position vector of a body at time is given by , find its displacement .

- A
- B
- C
- D

**Q5: **

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.

**Q6: **

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
- B
- C
- D
- E

**Q8: **

A person ran 160 m east and then 175 m north. Find the total distance covered by the person.

**Q9: **

A person rode a bicycle 7 km west and then 13 kmβ north of west. Find the total distance covered by the person.

**Q10: **

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
- C 375 meters, north of east
- D meters, south of east
- E meters, north of east

**Q11: **

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 .

- A ,
- B ,
- C ,
- D ,

**Q12: **

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.

- A 975 m, south of east
- B m, north of west
- C m, north of west
- D 450 m, north of east

**Q13: **

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
- B
- C
- D
- E

**Q14: **

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 manβs house from the supermarket
- Ethe displacement of the supermarket from the manβs house

**Q15: **

You traveled 213 miles from California to San Francisco. Does the β213 milesβ represent distance or displacement?

- ADisplacement
- BDistance

**Q16: **

If you were lost in a forest, would you prefer to know your distance or your displacement from the nearest settlement?

- Adistance
- Bdisplacement

**Q17: **

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.

**Q18: **

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.

**Q20: **

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 .

- A
- B
- C
- D2
- E1