1. An object has moved through a distance. Can it have zero displacement? If yes, support your answer with an example.
Ans:Yes, an object which has moved through a distance can have zero displacement if it comes back to its initial position.
Example: If a person jogs in a circular park which is circular and completes one round. His initial and final position is the same.
Hence, his displacement is zero.
2. A farmer moves along the boundary of a square field of side 10m in 40 s. What will be the magnitude of displacement of the farmer at the end of 2 minutes 20 seconds from his initial position?
Ans:
Given:
Side of the square field = 10m
Perimeter of the square = 40m
Time taken by the farmer to cover the boundary of 40m = 40s
So, in 1s, the farmer covers a distance of 1m
Now,
Time = 2 minutes 20 seconds = 140 seconds
Distance covered by the farmer in 140 seconds = 1m/s × 140s = 140m
The total number of rotations taken by the farmer to cover a distance of 140m:
Total distance / Perimeter = 140m / 40m = 3.5
At this point, the farmer is at point B from the origin O, halfway through the fourth side of the square field.
Using the Pythagorean theorem, the displacement :
s = √(102+102)
s = 10√2
s = 14.14 m
3. Which of the following is true for displacement?
(a) It cannot be zero.
(b) Its magnitude is greater than the distance travelled by the object.
Ans:
Neither of the statements is true.
(a) The given statement is false because the displacement of an object that travels a certain distance and returns to its initial position is zero.
(b) The given statement is false because the displacement of an object can be equal to the distance travelled but can never be greater than the distance travelled.
4. Distinguish between speed and velocity.
5.Under what condition(s) is the magnitude of average velocity of an object equal to its average speed?
Ans: The magnitude of average velocity and average speed will be the same when the total distance travelled is equal to the total displacement.
This occurs when the object moves in a straight line in a single direction without changing its path.
6. What does the odometer of an automobile measure?
Ans:
An odometer, or odograph, is a device that measures the total distance travelled by an automobile. It calculates this based on the perimeter of the wheel and the number of rotations made by the wheel.
7. What does the path of an object look like when it is in uniform motion?
Ans: The path of an object in uniform motion is a straight line.
8. During an experiment, a signal from a spaceship reached the ground station in five minutes. What was the distance of the spaceship from the ground station? The signal travels at the speed of light, that is, 3 × 108 m/s.
Ans:
Given that the signal travels in a straight line, the distance between the spaceship and the ground station is equal to the total distance travelled by the signal.
5 minutes = 5×60 seconds = 300 seconds.
Speed of the signal = 3 × 108 m/s.
Therefore, total distance = (3 × 108 m/s) x 300s
= 9×1010 meters.