# 3 Lecture

## Kinematics – II

Kinematics is the study of the motion of objects without considering the forces that cause the motion. In Kinematics – I, we learned about the basic concepts of motion, including distance, displacement, speed, velocity, and acceleration.

## Important Mcq's Midterm & Finalterm Prepration Past papers included

A car moves in a circular path of radius 100 meters with a constant speed of 10 m/s. What is the magnitude of the centripetal acceleration of the car?

A. 1 m/s²

B. 10 m/s²

C. 100 m/s²

D. 1000 m/s²

A ball is thrown horizontally from the top of a cliff with a speed of 20 m/s. If the cliff is 50 meters high, how far from the base of the cliff will the ball hit the ground?

A. 100 m

B. 150 m

C. 200 m

D. 250 m

A person is standing at the edge of a cliff and throws a ball with a velocity of 30 m/s at an angle of 60 degrees with the horizontal. What is the horizontal component of the velocity of the ball?

A. 15 m/s

B. 25 m/s

C. 30 m/s

D. 35 m/s

A car is traveling at a speed of 20 m/s and comes to a complete stop in 5 seconds. What is the magnitude of its acceleration?

A. 4 m/s²

B. 5 m/s²

C. 10 m/s²

D. 20 m/s²

A ball is thrown vertically upwards with a speed of 20 m/s. What is the maximum height reached by the ball?

A. 20 m

B. 40 m

C. 80 m

D. 160 m

A train is moving with a velocity of 40 m/s. If the train accelerates uniformly at 4 m/s² for 10 seconds, what is the final velocity of the train?

A. 80 m/s

B. 60 m/s

C. 50 m/s

D. 44 m/s

A car starts from rest and accelerates uniformly at 5 m/s² for 10 seconds. What is the distance traveled by car?

A. 125 m

B. 250 m

C. 500 m

D. 1000 m

A stone is thrown from the top of a building with an initial velocity of 20 m/s at an angle of 30 degrees with the horizontal. What is the range of the stone?

A. 20 m

B. 40 m

C. 60 m

D. 80 m

A rocket is launched vertically upwards with an initial velocity of 100 m/s. What is the maximum height reached by rocket?

A. 5000 m

B. 10000 m

C. 15000 m

D. 20000 m

A ball is thrown horizontally from the top of a building with a velocity of 10 m/s. If the building is 100 meters high, how far from the base of the building will the ball hit the ground?

A. 10 m

B. 20 m

C. 50 m

D. 100 m

## Subjective Short Notes Midterm & Finalterm Prepration Past papers included

What is projectile motion?

Answer: Projectile motion is the motion of an object that is thrown, launched, or dropped near the Earth's surface and moves along a curved path under the influence of gravity.

What are the two components of motion in projectile motion?

Answer: The two components of motion in projectile motion are the horizontal and vertical components.

What is the equation of motion for projectile motion in the x direction?

Answer: The equation of motion for projectile motion in the x direction is x = x0 + v0xt, where x is the final position, x0 is the initial position, v0x is the initial velocity in the x direction, and t is the time elapsed.

What is the equation of motion for projectile motion in the y direction?

Answer: The equation of motion for projectile motion in the y direction is y = y0 + v0yt - 1/2gt^2, where y is the final position, y0 is the initial position, v0y is the initial velocity in the y direction, g is the acceleration due to gravity, and t is the time elapsed.

What is circular motion?

Answer: Circular motion is the motion of an object along a circular path.

What is centripetal force?

Answer: Centripetal force is the force acting on an object that causes the circular motion and is directed toward the center of the circle.

What is the relationship between centripetal force, mass, velocity, and radius?

Answer: The relationship between centripetal force, mass, velocity, and radius is F = mv^2/r.

What is the period of the circular motion?

Answer: The period of circular motion is the time taken for one complete revolution around the circle.

What is the frequency of circular motion?

Answer: The frequency of circular motion is defined as the number of revolutions per unit of time.

How are period and frequency related?

Answer: Period and frequency are related by T = 1/f, where T is the period and f is the frequency.

Kinematics is the study of the motion of objects without considering the forces that cause the motion. In Kinematics – I, we learned about the basic concepts of motion, including distance, displacement, speed, velocity, and acceleration. In Kinematics – II, we will learn about more advanced concepts, such as projectile motion and circular motion. Projectile motion is the motion of an object that is thrown, launched, or dropped near the Earth's surface and moves along a curved path under the influence of gravity. The object moves both horizontally and vertically. The horizontal component of the motion is constant, while the vertical component is accelerated due to the force of gravity. The two components of motion are independent of each other.

### To analyze projectile motion, we use the equations of motion in the x and y directions separately. In the x direction, the motion is uniform and the equation of motion is given by:

x = x0 + v0xt where x is the final position, x0 is the initial position, v0x is the initial velocity in the x direction, and t is the time elapsed.

### In the y direction, the motion is accelerated due to gravity, and the equation of motion is given by:

y = y0 + v0yt - 1/2gt^2 where y is the final position, y0 is the initial position, v0y is the initial velocity in the y direction, g is the acceleration due to gravity, and t is the time elapsed.

### Circular motion

Circular motion is the motion of an object along a circular path. In a circular motion, the object moves along the circumference of the circle at a constant speed. The direction of the velocity of the object changes continuously, and therefore, there is a change in the acceleration of the object. This change in acceleration is called centripetal acceleration and is directed toward the center of the circle. To analyze circular motion, we use the concept of centripetal force. The force acting on the object that causes the circular motion is called the centripetal force. The magnitude of the centripetal force is given by: F = mv^2/r where F is the centripetal force, m is the mass of the object, v is the velocity of the object, and r is the radius of the circular path. The centripetal force can be provided by various sources, such as tension in a string, gravitational force, or electrostatic force. The centripetal force is always perpendicular to the velocity of the object and directed toward the center of the circle. The time taken for one complete revolution around the circle is called the period of the circular motion and is denoted by T. The frequency of the circular motion is defined as the number of revolutions per unit of time and is denoted by f. The relationship between period and frequency is given by: T = 1/f In summary, Kinematics – II deals with advanced concepts of motion, such as projectile motion and circular motion. Projectile motion involves the motion of an object that is thrown, launched, or dropped and moves along a curved path under the influence of gravity. Circular motion involves the motion of an object along a circular path with a constant speed, where the direction of the velocity changes continuously. The centripetal force is the force that causes circular motion and is directed toward the center of the circle. The period and frequency of circular motion are related by T = 1/f. Understanding these concepts is essential in understanding the behavior of objects in motion and their applications in various fields, such as engineering and physics.