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In this lesson, we will learn how to differentiate between distance and displacement and how to find them.

Q1:

Using the given figure, calculate the distance π and the displacement π of a body that moves from point π΄ to point πΆ then returns to point π΅ .

Q2:

A particle moving in a straight line has a position vector β π , defined by the relation β π = ( π‘ + 3 ) β π 2 , where π‘ is the time, measured in seconds, and β π is a unit vector. Determine the magnitude of the displacement vector β π in metres 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.

Q4:

What kind of information does this signpost show?

Q5:

The position vector of a particle relative to the point π is given by the relation β π = ( π‘ + 4 π‘ β 5 ) β π 2 , where β π is a fixed unit vector and π‘ is the time. Find the displacement of the particle after 3 seconds.

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 6 0 β 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?

Q9:

The displacement of a particle of unit mass is given as a function of time by the relation β π ( π‘ ) = οΉ 3 5 π‘ β 2 π‘ ο β π 2 , where β π is constant unit vector, π measured in centimetres, and π‘ in seconds. Given that the particle started its motion at π‘ = 0 , find the total distance covered in the first 5 seconds of its motion.

Q10:

A car moved 1 5 0 m e t r e s east and then 2 2 5 m e - north. Find the magnitude and direction of its displacement, rounding the angle to the nearest minute.

Q11:

A bird leaves its nest and flies for 5 kilometres in the direction north of east before stopping to rest in a tree. It then flies 10 kilometres southeast from the tree, landing on top of a telephone pole. Given that the vector represents a displacement of 1 kilometre east and the vector represents a displacement of 1 kilometre north, find the vector that represents the displacement of the telephone pole from the nest.

Q12:

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

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 u and the displacement of the supermarket from the bank is represented by the vector v , what does the vector u v + represent?

Q14:

According to the figure, a body moved from π΄ to π΅ along the line segment π΄ π΅ , and then it moved to πΆ along π΅ πΆ . Finally, it moved to π· along πΆ π· and stopped there. Find the distance covered by the body π ο§ and the magnitude of its displacement π ο¨ .

Q15:

If the position vector of a body at time π‘ is given by β π ( π‘ ) = οΉ β 3 π‘ β 5 ο β π + ( β 4 π‘ β 6 ) β π 2 , find its displacement β π ( π‘ ) .

Q16:

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

Q17:

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

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