Distance and displacement – problems and solutions

1. A car travels along a straight road 100 m east then 50 m west. Find distance and displacement of the car.

Solution

__Distance is 100 met____ers + 50 meters = 150 meters__

__Displacement is 100 meters – 50 meters = 50 meters, to the east__.

2. A person walks 4 meters east, then walks 3 meters north. Determine distance and displacement.

Solution

3. A runner travels around rectangle track with length = 50 meters and width = 20 meters. After travels around rectangle track two times, runner back to starting point. Determine distance and displacement.

Solution

Circumference of rectangle = 2(50 meters) + 2(20 meters) = 100 meters + 40 meters = 140 meters.

Travels around rectangle 2 times = 2(140 meters) = 280 meters.

__Distance = 280 m__.

__Displacement = 0 m__. (the runner return to the starting point)

4. Car’s speedometer reads 10,500 km at the start of a trip and 10,700 km at the end. Determine distance and displacement.

Solution

Distance = 10,700 km – 10,500 km = 200 km.

Displacement = 0 km. (car return to the starting point)

**1. What is distance?** Answer: Distance is the total movement of an object, irrespective of the direction.

**2. What is displacement?** Answer: Displacement is the shortest distance between the initial and final position of an object, with a specified direction.

**3. Can distance ever be less than displacement?** Answer: No. Distance is always greater than or equal to displacement.

**4. If a person walks around a circular track and ends up at the starting point, what is the displacement?** Answer: The displacement is zero because the initial and final positions are the same.

**5. What is the unit of distance and displacement in the metric system?** Answer: Both are measured in meters (m).

**6. Can displacement be negative?** Answer: Yes. A negative displacement indicates the direction is opposite to the chosen positive direction.

**7. How are distance and displacement represented in vector form?** Answer: Distance is a scalar quantity and has only magnitude. Displacement, being a vector, has both magnitude and direction.

**8. If a person walks 10 meters east and then 10 meters west, what is the total distance covered and the total displacement?** Answer: Distance = 20 meters; Displacement = 0 meters.

**9. What does a zero displacement indicate?** Answer: It indicates that the initial and final positions are the same.

**10. Is it possible for an object to be in motion if its displacement is zero?** Answer: Yes. An object moving in a closed loop or path returns to its starting position, resulting in zero displacement.

**11. How is average speed calculated?** Answer: Average speed = Total distance traveled / Total time taken.

**12. How is average velocity calculated?** Answer: Average velocity = Total displacement / Total time taken.

**13. What is the significance of the direction in displacement?** Answer: The direction in displacement helps in understanding the orientation of movement from the initial to the final position.

**14. How do we denote displacement in a one-dimensional motion?** Answer: In one-dimensional motion, displacement can be represented by a positive or negative value, depending on the chosen reference direction.

**15. What would be the displacement for any object thrown upwards and then coming back to the thrower’s hand?** Answer: The displacement would be zero because the starting and ending positions are the same.

**16. Can the magnitude of displacement be greater than the distance traveled?** Answer: No. The magnitude of displacement can be equal to or less than the distance, but never greater.

**17. What role does the reference point play in determining displacement?** Answer: The reference point helps define the initial position from which displacement is calculated.

**18. If a car travels in a straight line for 50 kilometers and then returns to its starting point, what is its displacement?** Answer: The displacement is zero.

**19. What is the path length in the context of motion?** Answer: Path length is another term for distance traveled.

**20. How can you distinguish between distance and displacement graphically?** Answer: On a graph, distance is always represented by a non-decreasing curve, while displacement can be represented by a curve that increases, decreases, or remains constant, depending on the direction of movement.

**21. Is it necessary for an object to be in motion to have a displacement?** Answer: No. An object can have a displacement if its position changes, even if it isn’t in motion for some duration.

**23. If the total path covered by an object is curved, is the displacement still the shortest distance between the starting and ending points?** Answer: Yes, the displacement is always the straight line distance between the starting and ending points.

**24. In which situations can distance and displacement have the same magnitude?** Answer: When an object moves in a straight line without changing its direction.

**25. Can an object have a constant speed and a changing velocity?** Answer: Yes, if the object is moving in a curved path at a constant speed, its direction (and hence velocity) changes, but its speed remains constant.

**26. How do distance and displacement relate to time?** Answer: Distance and displacement, when divided by time, give average speed and average velocity, respectively.

**27. Can an object’s distance from a point increase while its displacement remains constant?** Answer: No. If the displacement remains constant, the object’s position relative to the starting point doesn’t change, so the distance from the point cannot increase.

**28. Is displacement a scalar or vector quantity?** Answer: Displacement is a vector quantity.

**29. Why can’t we add distances directly to get a resultant like displacements?** Answer: Because distance lacks direction, it represents only magnitude. Displacements have both magnitude and direction, so they can be added vectorially.

**30. In which motion is the displacement equal to the circumference of the circle?** Answer: In circular motion, if one complete revolution is made, the distance is equal to the circumference, but the displacement is zero. Only if the motion covers exactly half of the circle, the displacement (a straight line through the circle’s diameter) would be equal to the circle’s radius.