# Worksheet: Distance and Displacement

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:

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.

Q3:

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 450 m, north of east
• C m, north of west
• D m, north of west

Q4:

What kind of information does this signpost show?

• Aspeed
• Bdistance
• Cvelocity
• Ddisplacement

Q5:

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

Q6:

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

Q7:

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

Q8:

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

• Bdistance

Q9:

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.

• A 141.25 cm
• B 28.12 cm
• C 278.12 cm
• D 181.25 cm

Q10:

A car moved 150 meters east and then 225 meters north. Find the magnitude and direction of its displacement, rounding the angle to the nearest minute.

• A meters, south of east
• B meters, north of east
• C meters, north of west
• D meters, north of east
• E375 meters, north of east

Q11:

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

Q12:

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.

• A 40 m
• B 6 m
• C 12 m
• D 5 m

Q13:

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 manβs house from the supermarket
• Bthe total distance the man traveled to the supermarket
• Cthe displacement of the supermarket from the bank
• Dthe displacement of the supermarket from the manβs house
• Ethe displacement of the bank from the supermarket

Q14:

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 ,

Q15:

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

• A
• B
• C
• D

Q16:

What is the name of the vector quantity which gives the total change of a particleβs position?

• Avelocity vector
• Bdistance
• Cacceleration vector
• Ddisplacement

Q17:

You traveled 213 miles from California to San Francisco. Does the β213 milesβ represent distance or displacement?