Average Velocity is a Vector Quantity Which can be either positive or negative depending on the direction of the object's motion.

equations of motion are valid only when acceleration is constant, and motion is constrained to a straight line.

The internal forces in an exploding bomb are the forces that cause the bomb to break apart. These forces are typically very large, as they must be able to overcome the strong bonds that hold the bomb together.

The external gravitational force, on the other hand, is much smaller. This is because the gravitational force is proportional to the mass of the bomb, and the mass of the bomb is small compared to the Earth.

The concept of "state of rest" and "state of motion" are relative, meaning that they depend on the reference frame of the observer.

In physics, a reference frame is a set of coordinates used to describe the position and orientation of objects in space. Different reference frames can be used to describe the same physical system, and the state of rest or motion of an object will depend on the reference frame being used.

For example, consider an object that is stationary relative to a stationary reference frame. From the perspective of an observer in this reference frame, the object is in a state of rest. However, from the perspective of an observer in a reference frame that is moving relative to the first reference frame, the object may appear to be in motion.

The inertia of an object causes the object to resist any change in the state of its motion.

The average speed of an object is always positive because speed is defined as the distance traveled per unit of time, and distance is always a positive quantity. Therefore, the speed of an object will always be positive as well.

When the projectile reaches a vertical velocity of zero, this is the maximum height of the projectile and then gravity will take over and accelerate the object downward.

The horizontal displacement of the projectile is called the range of the projectile, and depends on the initial velocity of the object.

A projectile have a minimum speed at the highest point of its trajectory. This is because horizontal speed of the projectile remains constant. Since the only force exerted on the projectile is gravity, which is 9.8
m/s2 acting downwards and has no effects on the horizontal velocity.

To calculate the impulse applied to the ball by the bat, we need to use the formula:

Impulse = Change in momentum

We can also rearrange the formula to solve for the change in momentum:

Change in momentum = Impulse

In this case, the mass of the ball is 0.163 kg and the change in velocity of the ball is +47 m/s - (-36 m/s) = +83 m/s. We can use these values to calculate the change in momentum of the ball:

Change in momentum = Mass * Change in velocity
= 0.163 kg * 83 m/s
= 13.6 Ns

All three equations of motion (also known as the laws of motion) are only applicable if the motion of the object is uniform, meaning that the acceleration of the object is constant.

The three equations of motion, which were formulated by Sir Isaac Newton, are as follows:

1. The first law of motion: This law states that an object will remain at rest or in motion at a constant velocity unless acted upon by an external force. This is also known as the law of inertia.
2. The second law of motion: This law states that the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass. Mathematically, this can be expressed as: F = ma, where F is the force applied, m is the mass of the object, and a is the acceleration of the object.
3. The third law of motion: This law states that for every action, there is an equal and opposite reaction. This means that if one object exerts a force on a second object, the second object will exert an equal and opposite force on the first object.

These laws are only applicable if the motion of the object is uniform, meaning that the acceleration of the object is constant. If the acceleration of the object is not constant, then the laws of motion may not hold.

Real collisions between macroscopic objects are usually inelastic but some collisions, such as those between steel ball bearings or between billiard balls are elastic.

The instantaneous velocity will increase with time. If the motion is accelerated, no matter if the acceleration is constant, or variable, the instantaneous velocity will increase. Variation of acceleration describes how to change in velocity is changing.

Inertia is the resistance offered by a body to the motion greater the mass Greater will be its inertia.

Here are a few examples to illustrate how inertia works:

• If you try to push a heavy suitcase across the floor, it will be difficult to get it moving because it has a lot of inertia. However, once it is moving, it will be easier to keep it moving because it has momentum.
• If you are driving a car and you need to stop quickly, it will be harder to do so if you are driving a car with a lot of mass (such as a truck) because the car has more inertia.
• If you are on a skateboard and you try to stop suddenly, it will be easier to do so because the skateboard has less mass and therefore less inertia.

The maximum range of a projectile is achieved when it is thrown at an angle of 45 degrees. This is because at this angle, the projectile spends the most time in the air and has the most time to travel before it falls back to the ground.

If two objects of different masses are traveling at the same velocity, the object with the larger mass will exert a greater force, according to the equation

F = ma

(where F is the force, m is the mass, and a is the acceleration).

Since the acceleration of the two objects is the same (due to their equal velocities), the only factor affecting the force they exert is their mass. Therefore, the object with the larger mass will exert a greater force.

Gravity provides a constant acceleration g towards the center of the Earth (the negative y-direction). Since gravity acts vertically, there is no acceleration in the horizontal (x) direction. This special type of two-dimensional motion is called projectile motion.

Acceleration is a vector in the same direction as the change in velocity, Δv. Since velocity is a vector, it can change either in magnitude or in direction. Acceleration is therefore a change in either speed or direction, or both.

Instantaneous Acceleration

It is the acceleration at any instant and is defined as the limiting vaue of the average acceleration when the time interval Δt becomes very small.

The gradient (or slope) of a velocity-time graph is called acceleration.

In a velocity-time graph, the horizontal axis represents time and the vertical axis represents velocity. The gradient of the graph at any point is equal to the acceleration of the object at that time. A positive gradient indicates that the acceleration of the object is positive (i.e., the velocity is increasing), while a negative gradient indicates that the acceleration of the object is negative (i.e., the velocity is decreasing).

The horizontal velocity of a projectile is constant (a never changing in value), There is a vertical acceleration caused by gravity; its value is 9.8 m/s/s, down, The vertical velocity of a projectile changes by 9.8 m/s each second, The horizontal motion of a projectile is independent of its vertical motion.

The second law of motion states that the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass. Mathematically, this can be expressed as: F = ma, where F is the force applied, m is the mass of the object, and a is the acceleration of the object.

When the sum of two angles is 90°, then the angles are known as complementary angles. In other words, if two angles add up to form a right angle, then these angles are referred to as complementary angles.

The average velocity of an object is calculated by dividing the distance traveled by the time taken to travel that distance. In this case, the object moves a distance of 10 meters to the right in 5 seconds, giving an average velocity of 10 meters / 5 seconds = 2 meters per second to the right.

Distance

Distance is a scalar quantity because it has only magnitude and no direction. It is a measure of how much ground an object has covered, regardless of the direction of travel.

Velocity

Velocity is a measure of how fast an object is moving and in what direction it is moving. For example, a car traveling at 50 km/h to the north and a car traveling at 50 km/h to the south have different velocities because they are moving in different directions.

Displacement

Displacement is a measure of how much an object has moved from its starting position. It is a vector quantity because it includes both the magnitude of the movement and the direction in which the object has moved.

Impulse

Impulse is the change in momentum of an object over a period of time. It is a vector quantity because it includes both the magnitude of the change in momentum and the direction in which the momentum has changed.

The rate of change of velocity is called acceleration. Acceleration is the ratio of change in velocity with time. The SI unit of acceleration is m/s².

The area under the line on a velocity-time graph is equal to the displacement of the object.

When two forces act on an object in opposite directions and have equal magnitudes, they will cancel each other out and produce a net force of zero on the object. This means that the object will not experience any acceleration or change in velocity as a result of the forces.

For the accelerated motion of an object along a straight line, a non-zero force must be acting on the object, which is increasing its velocity and speed. However, the direction of force is not given so it can’t be determined whether it is moving away from earth or not.

An inelastic collision is one where the objects collide and stick together without bouncing apart. A head-on collision is one where the two objects approach each other from opposite directions, 180° apart. It may or may not be elastic.

Linear momentum points in the same direction as the velocity of the object.

Linear momentum is a measure of the motion of an object, and it is a vector quantity, which means it has both magnitude and direction. The magnitude of the linear momentum is determined by the mass and velocity of the object, and the direction is determined by the velocity of the object.

For example,
if an object is moving to the right at a certain speed, its linear momentum will be directed to the right. If the object slows down or changes direction, its linear momentum will also change accordingly.

In the absence of air resistance, a light object and a heavy object will have the same acceleration when subjected to the same force. This is because the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass, according to the second law of motion (F = ma).

For example,

if two objects are dropped from the same height, one object with a mass of 1 kilogram and the other object with a mass of 10 kilograms, and both objects are subjected to the same gravitational force (9.8 Newtons), the acceleration of both objects will be the same. The acceleration of the objects will be 9.8 meters per second squared, regardless of their mass

The horizontal distance travelled by a projectile is called its range.

A rocket works by expelling gases at high velocity, causing it to accelerate in the opposite direction due to the conservation of momentum. This is described by Newton's third law of motion, which states that "For every action, there is an equal and opposite reaction." The action is the expulsion of the gases, and the reaction is the acceleration of the rocket. The total momentum of the system (rocket + expelled gases) remains constant, but the momentum of the rocket increases while the momentum of the gases decreases by an equal amount.

The direction of the impulse is the same as the direction of the force acting on the object. This is because the force applied to an object causes a change in its momentum, and the direction of that change determines the direction of the impulse.

To put it simply, the impulse has the same direction as the force because it is the result of the force acting on the object.

The law of inertia is the first law of motion formulated by Sir Isaac Newton. It states that an object will remain at rest or in motion at a constant velocity unless acted upon by an external force.

During a collision, the kinetic energy of the objects is converted into other forms of energy, such as heat, sound, and deformation. This energy transfer can cause the objects to exert very strong forces on each other, which can be much larger than any external forces that may be acting on them.

For example,
if two cars collide at high speed, the forces exerted during the collision can be much stronger than the gravitational force acting on the cars (which is an external force). As a result, the forces due to the collision are generally assumed to be larger than any external forces present.

The negative sign indicates that the force is acting in the opposite direction to the motion, which is consistent with the car's velocity decreasing.

if an object is moving with uniform acceleration, the average acceleration over any time interval is equal to the instantaneous acceleration at any point during that interval. This is because the acceleration is constant and the change in velocity is also constant over the interval.

if we take Exact Line of Book then 2 is correct other than Motion mechanics can be sub-divided into several types, including translational motion, rotational motion, and oscillatory motion.

Momentum (P): The product of mass and velocity is called momentum.

The SI unit of momentum is kg m/s.

Momentum (P) = Mass (m) × Velocity (v)

A shell exploding into fragments:
Initial momentum of the shell is conserved as fragments move in different directions.

Falling bomb exploding into two pieces:
Momentum of the falling bomb is conserved when it explodes into two pieces.

Firing of a gun:
Total momentum is conserved as the gun imparts forward momentum to the bullet, while the gun experiences equal and opposite backward momentum.

Impulse is the product of force and time (J = F*t),
and it is equal to the change in momentum of an object.

This relationship can be expressed mathematically as J = p2 - p1, where J is the impulse, p1 is the initial momentum of the object, and p2 is the final momentum of the object.

The rate of change of linear momentum of a body is equal to the force acting on it

(F = dp/dt).

to remember this is to think of the slope as a "rise over run" ratio, just as it is in a traditional slope calculation. If the slope is increasing, it means that the "rise" (i.e., the change in displacement) is increasing faster than the "run" (i.e., the change in time), resulting in a larger slope and a higher velocity. which show object is accelerating.

The slope of the tangent to a curve at a particular point is the instantaneous rate of change of the function at that point

Projectiles accelerate in the vertical direction at 9.8 m/s/s. Since acceleration is the rate at which the velocity changes, this acceleration means that the vertical velocity of a projectile changes by 9.8 m/s each second.

The velocity of the horizontal component of the projectile motion is constant because there is no external force which acts on the horizontal component of the velocity, but the external force acts on the vertical component of the velocity.

decrease in mass is due to the loss of gases, not the velocity of the gases. The mass of the rocket would also decrease if it lost any other kind of matter, such as fuel or water, regardless of the velocity at which it was expelled.