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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?
![Check Mark](/static/check-mark.png)
(a)
The displacement of the cyclist.
Answer to Problem 3.1CYU
The displacement of the cyclist is −1 km.
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,
Δx=xf−xi
Where,
xf is the final position of the body.
xi is the initial position of the body.
Also, when there is a series of displacement, then total displacement is equal to the sum of individual displacements and it is written as,
ΔxT=∑Δxi
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 −3 km. So, the displacement for the first case will be,
Δx1=(−3)−0=−3 km
After travelling 3 km towards west, cyclist turns around and travels 2 km towards east. Now, the initial position of cyclist is −3 km and final position is −1 km. So, the displacement for the second case will be,
Δx1=(−1)−(−3)=−1+3=2 km
The total displacement will be,
ΔxT=Δx1+Δx2=−3+2=−1 km
Conclusion:
Therefore, the displacement of the cyclist is −1 km.
![Check Mark](/static/check-mark.png)
(b)
The distance travelled by the cyclist.
Answer to Problem 3.1CYU
The distance travelled by the cyclist is 5 km.
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, ΔxTD=∑|Δxi|
Calculation:
The displacement for the first case is,
Δx1=−3 km
The displacement for the second case is,
Δx2=2 km
The total distance travelled is,
ΔxTD=|Δx1|+|Δx2|=|−3|+|2|=3+2=5 km
Conclusion:
Therefore, the distance travelled by the cyclist is 5 km.
![Check Mark](/static/check-mark.png)
(c)
The magnitude of the displacement.
Answer to Problem 3.1CYU
The magnitude of displacement of the cyclist is 1 km.
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,
Δx=xf−xi
Where,
xf is the final position of the body.
xi is the initial position of the body.
Also, when there is a series of displacement, then total displacement is equal to the sum of individual displacements and it is written as,
ΔxT=∑Δxi
Calculation:
The displacement for the first case is,
Δx1=−3 km
The displacement for the second case is,
Δx2=2 km
The total displacement will be,
ΔxT=Δx1+Δx2=−3+2=−1 km
Magnitude of displacement is,
|ΔxT|=|−1|=1 km
Conclusion:
Therefore, the magnitude of displacement of the cyclist is 1 km.
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