Check your Understanding A cyclist rides 3 km west and then tune around and tides 2 kin east. (a) What Is his displacement? (b) What is the distance traveled? (c) What is the magnitude of his displacement?
(a)
The displacement of the cyclist.
Answer to Problem 3.1CYU
The displacement of the cyclist is
Explanation of Solution
Given:
Initially cyclist travel towards west and covers 3 km and then he turned towards east and travelled covering 2 km.
Formula used:
Displacement is defined as the change in position of an object. Numerically it is written as,
Where,
Also, when there is a series of displacement, then total displacement is equal to the sum of individual displacements and it is written as,
Calculation:
Consider that the cyclist starts from origin and east direction will be positive.
Initially cyclist moves 3 km towards west. The initial position of cyclist is 0 km and final position of cyclist is
After travelling 3 km towards west, cyclist turns around and travels 2 km towards east. Now, the initial position of cyclist is
The total displacement will be,
Conclusion:
Therefore, the displacement of the cyclist is
(b)
The distance travelled by the cyclist.
Answer to Problem 3.1CYU
The distance travelled by the cyclist is
Explanation of Solution
Given:
Initially cyclist travel towards west and covers 3 km and then he turned towards east and travelled covering 2 km.
Formula used:
Distance travelled by an object is equal to the sum of magnitudes of individual displacements,
Calculation:
The displacement for the first case is,
The displacement for the second case is,
The total distance travelled is,
Conclusion:
Therefore, the distance travelled by the cyclist is
(c)
The magnitude of the displacement.
Answer to Problem 3.1CYU
The magnitude of displacement of the cyclist is
Explanation of Solution
Given:
Initially cyclist travel towards west and covers 3 km and then he turned towards east and travelled covering 2 km.
Formula used:
Displacement is defined as the change in position of an object. Numerically it is written as,
Where,
Also, when there is a series of displacement, then total displacement is equal to the sum of individual displacements and it is written as,
Calculation:
The displacement for the first case is,
The displacement for the second case is,
The total displacement will be,
Magnitude of displacement is,
Conclusion:
Therefore, the magnitude of displacement of the cyclist is
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