# Worksheet: Position, Displacement, and Distance

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

Q1:

Using the given figure, calculate the distance and the displacement of a body that moves from point to point then returns to point . • A,
• B,
• C,
• D,

Q2:

What kind of information does this signpost show? • Bvelocity
• Cdisplacement
• Dspeed

Q3:

What is the name of the vector quantity which gives the total change of a particle’s position?

• 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

Q7:

A particle started moving in a straight line. After seconds, its position relative to a fixed point is given by Find the displacement of the particle during the first five seconds.

• A5 m
• B6 m
• C40 m
• D12 m

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 km 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
• C375 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.

• A975 m, south of east
• B m, north of west
• C m, north of west
• D450 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 man’s house from the supermarket
• Ethe displacement of the supermarket from the man’s house

Q15:

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

• BDistance

Q16:

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

• 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.

Q19:

Using point and direction vector , give the position vector of the point on this line corresponding to parameter .

• A
• B
• C
• D

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