Motion is an essential concept in physics, and class 9 students often face numerical problems related to it. Understanding the principles of motion and how to solve numerical questions is crucial for excelling in exams. This article aims to provide you with a comprehensive collection of numerical questions and their step-by-step solutions on motion for class 9.
Numerical Questions and Answers on Motion for Class 9
Let’s delve into the world of motion with these exciting numerical questions and answers:
1. Speed, Velocity, and Acceleration
Q: A car travels at a constant speed of 60 km/h for 2 hours. What is the total distance covered by the car?
A: To find the distance, we can use the formula: distance = speed × time. So, distance = 60 km/h × 2 hours = 120 km.
Q: A cyclist accelerates from rest at 2 m/s². How long will it take the cyclist to reach a velocity of 10 m/s?
A: We can use the formula: time = (final velocity – initial velocity) / acceleration. Time = (10 m/s – 0) / 2 m/s² = 5 seconds.
2. Motion under Gravity
Q: An object is dropped from a height of 80 meters. Calculate its velocity when it hits the ground.
A: We can use the formula: final velocity = √(2 × acceleration due to gravity × height). Assuming the acceleration due to gravity as 9.8 m/s², the velocity will be √(2 × 9.8 m/s² × 80 m) ≈ 39.2 m/s.
Q: A ball is thrown vertically upwards with a velocity of 20 m/s. Calculate the maximum height it will reach.
A: The maximum height can be calculated using the formula: maximum height = (initial velocity)² / (2 × acceleration due to gravity). Substituting the values, we get: maximum height = (20 m/s)² / (2 × 9.8 m/s²) ≈ 20.41 meters.
3. Projectile Motion
Q: An object is thrown at an angle of 30 degrees with the horizontal and a velocity of 20 m/s. Determine the maximum height it will reach. (g =10 m/s^2)
A: To find the maximum height, we can use the formula:
maximum height = [initial velocity × sin(angle)]2 / (2 × acceleration due to gravity).
Substituting the values, we get: maximum height = [20 m/s × sin(30 degrees)]2 / (2 × 10 m/s²) = 100/20 m = 5 m
4. Uniform Circular Motion
Q 1: A car is moving in a circle with a radius of 100 meters at a constant speed of 10 m/s. Calculate the centripetal acceleration.
If the centripetal force acting on the car is 500 N, what is the mass of the car?
A: Centripetal acceleration can be calculated using the formula: centripetal acceleration = (velocity)^2 / radius. Substituting the values, we get: centripetal acceleration = (10 m/s)² / 100 meters = 1 m/s².
We know that centripetal force = (mass × centripetal acceleration). Rearranging the formula, we get: mass = centripetal force / centripetal acceleration. Substituting the values, we get: mass = 500 N / 1 m/s² = 500 kg.
5. Relative Motion
Q: Two cars are moving in the same direction with speeds of 50 km/h and 60 km/h, respectively. Calculate the relative velocity of the second car with respect to the first car.
A: Relative velocity of the second car with respect to the first car can be calculated by subtracting the speed of the first car from the speed of the second car. So, relative velocity = 60 km/h – 50 km/h = 10 km/h.
Q: If two objects are moving in opposite directions and have velocities of 15 m/s and 25 m/s, respectively, what is their relative velocity?
A: When moving in opposite directions, the relative velocity is the sum of their individual velocities. So, relative velocity = 15 m/s + 25 m/s = 40 m/s.
Frequently Asked Questions (FAQs)
- Q: What are the key principles of motion?
A: The key principles of motion are speed, velocity, acceleration, and the laws of motion formulated by Sir Isaac Newton. - Q: How can I calculate the acceleration of an object?
A: Acceleration can be calculated using the formula: acceleration = (change in velocity) / time. - Q: What is the difference between speed and velocity?
A: Speed is a scalar quantity that only considers magnitude, while velocity is a vector quantity that considers both magnitude and direction. - Q: Can you explain the concept of projectile motion?
A: Projectile motion is the motion of an object thrown or projected into the air and moving under the influence of gravity alone. - Q: How do we represent uniform circular motion on a graph?
A: Uniform circular motion is represented by a constant-radius circle on a position-time graph. - Q: What is relative motion?
A: Relative motion is the motion of an object as observed from a particular point of reference.
Conclusion
In this article, we explored numerical questions and answers on motion for class 9, covering various aspects of motion, such as speed, velocity, acceleration, motion under gravity, projectile motion, uniform circular motion, and relative motion. By practicing these numerical problems, students can strengthen their understanding of motion and perform better in their exams.
Remember, practice makes perfect, and understanding the principles of motion is the key to mastering this fundamental concept in physics.
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