Kanjit Ran 3.5 Km [E], Turned Around, And Ran Another 5.8 Km [W] In 50 Minutes. A. What Is Kanjit's Total Displacement? B. What Is Kanjit's Total Distance Traveled? C. What Is His Average Velocity In M/s? D. What Is His Average Speed, In M/s?

Mar 13, 2025 by ADMIN 244 views

**Understanding Displacement, Distance, Velocity, and Speed in Physics**

Introduction

In physics, displacement and distance are two fundamental concepts that are often confused with each other. Displacement refers to the change in position of an object from its initial to its final position, whereas distance refers to the total length of the path traveled by an object. In this article, we will explore these concepts through a real-life scenario involving Kanjit, who ran 3.5 km east and then 5.8 km west in 50 minutes.

Problem Statement

Kanjit ran 3.5 km east and then turned around and ran 5.8 km west in 50 minutes. We need to find:

a. Kanjit's total displacement b. Kanjit's total distance traveled c. Kanjit's average velocity in m/s d. Kanjit's average speed in m/s

Solution

a. Total Displacement

To find the total displacement, we need to find the final position of Kanjit relative to his initial position. Since Kanjit ran 3.5 km east and then 5.8 km west, we can find the net displacement by subtracting the westward distance from the eastward distance.

eastward_distance = 3.5 km
westward_distance = 5.8 km
net_displacement = eastward_distance - westward_distance

However, since Kanjit ran in the opposite direction, we need to take the absolute value of the net displacement to find the total displacement.

total_displacement = abs(net_displacement)

b. Total Distance Traveled

To find the total distance traveled, we simply add the eastward and westward distances.

total_distance = eastward_distance + westward_distance

c. Average Velocity

To find the average velocity, we need to find the change in position (displacement) and divide it by the time taken.

time_taken = 50 minutes
average_velocity = total_displacement / (time_taken / 60)  # convert minutes to hours

d. Average Speed

To find the average speed, we need to find the total distance traveled and divide it by the time taken.

average_speed = total_distance / (time_taken / 60)  # convert minutes to hours

Calculations

Now, let's plug in the values and calculate the answers.

a. Total Displacement

eastward_distance = 3.5 km
westward_distance = 5.8 km
net_displacement = eastward_distance - westward_distance
net_displacement = -2.3 km
total_displacement = abs(net_displacement)
total_displacement = 2.3 km

b. Total Distance Traveled

total_distance = eastward_distance + westward_distance
total_distance = 3.5 km + 5.8 km
total_distance = 9.3 km

c. Average Velocity

time_taken = 50 minutes
average_velocity = total_displacement / (time_taken / 60)  # convert minutes to hours
average_velocity = 2.3 km / (50 / 60)  # convert minutes to hours
average_velocity = 2.76 m/s

d. Average Speed

average_speed = total_distance / (time_taken / 60)  # convert minutes to hours
average_speed = 9.3 km / (50 / 60)  # convert minutes to hours
average_speed = 11.16 m/s

Conclusion

In conclusion, Kanjit's total displacement is 2.3 km, his total distance traveled is 9.3 km, his average velocity is 2.76 m/s, and his average speed is 11.16 m/s.

Key Takeaways

Displacement refers to the change in position of an object from its initial to its final position.
Distance refers to the total length of the path traveled by an object.
Average velocity is the change in position (displacement) divided by the time taken.
Average speed is the total distance traveled divided by the time taken.

Real-World Applications

Understanding displacement, distance, velocity, and speed is crucial in various fields such as physics, engineering, and transportation. For example, in navigation, understanding displacement and distance is essential for determining the position and trajectory of an object. In transportation, understanding velocity and speed is crucial for determining the time and distance traveled by a vehicle.

Final Thoughts

Q: What is the difference between displacement and distance?

A: Displacement refers to the change in position of an object from its initial to its final position, whereas distance refers to the total length of the path traveled by an object.

Q: How do you calculate displacement?

A: To calculate displacement, you need to find the final position of an object relative to its initial position. If the object moves in a straight line, you can simply subtract the initial position from the final position. If the object moves in a curved path, you need to use the Pythagorean theorem to find the displacement.

Q: What is the formula for calculating displacement?

A: The formula for calculating displacement is:

d = √((x2 - x1)^2 + (y2 - y1)^2)

where d is the displacement, (x1, y1) is the initial position, and (x2, y2) is the final position.

Q: How do you calculate distance?

A: To calculate distance, you need to find the total length of the path traveled by an object. If the object moves in a straight line, you can simply add the lengths of the individual segments. If the object moves in a curved path, you need to use the Pythagorean theorem to find the distance.

Q: What is the formula for calculating distance?

A: The formula for calculating distance is:

s = √((x2 - x1)^2 + (y2 - y1)^2)

where s is the distance, (x1, y1) is the initial position, and (x2, y2) is the final position.

Q: What is the difference between velocity and speed?

A: Velocity is a vector quantity that describes the rate of change of an object's position with respect to time, whereas speed is a scalar quantity that describes the rate of change of an object's distance with respect to time.

Q: How do you calculate velocity?

A: To calculate velocity, you need to find the change in position (displacement) and divide it by the time taken.

Q: What is the formula for calculating velocity?

A: The formula for calculating velocity is:

v = Δx / Δt

where v is the velocity, Δx is the displacement, and Δt is the time taken.

Q: How do you calculate speed?

A: To calculate speed, you need to find the total distance traveled and divide it by the time taken.

Q: What is the formula for calculating speed?

A: The formula for calculating speed is:

s = Δs / Δt

where s is the speed, Δs is the distance traveled, and Δt is the time taken.

Q: What is the difference between average velocity and average speed?

A: Average velocity is the change in position (displacement) divided by the time taken, whereas average speed is the total distance traveled divided by the time taken.

Q: How do you calculate average velocity?

A: To calculate average velocity, you need to find the change in position (displacement) and divide it by the time taken.

Q: What is the formula for calculating average velocity?

A: The formula for calculating average velocity is:

v_avg = Δx / Δt

where v_avg is the average velocity, Δx is the displacement, and Δt is the time taken.

Q: How do you calculate average speed?

A: To calculate average speed, you need to find the total distance traveled and divide it by the time taken.

Q: What is the formula for calculating average speed?

A: The formula for calculating average speed is:

s_avg = Δs / Δt

where s_avg is the average speed, Δs is the distance traveled, and Δt is the time taken.

Conclusion

In conclusion, displacement, distance, velocity, and speed are all important concepts in physics that are used to describe the motion of objects. Understanding these concepts is crucial for solving problems in physics and engineering. We hope this article has provided valuable insights into these concepts and will inspire readers to explore this fascinating subject further.