when the object is moving, and the distance is increasing over time.

When the stone is released, it has a horizontal velocity component due to the moving train and a vertical component due to gravity.

The combination of these two motions - linear horizontal motion and accelerated vertical motion due to gravity - results in a parabolic trajectory.

line passing through the origin. The slope of the line is equal to the velocity of the object, and the direction of the line indicates the direction of motion of the object.

important
When a body has zero acceleration, its velocity is constant. The instantaneous velocity and average velocity of a moving object are equal when the object is moving at a constant velocity.
Basics You Must Know

Instantaneous velocity refers to the velocity of an object at a specific point in time, while average velocity is the total displacement of an object over a period of time, divided by that time interval.

When a body has zero acceleration and is moving at a constant velocity, its displacement over any given time interval will be proportional to that time interval. Therefore, the ratio of displacement to time will be the same for any time interval, making the instantaneous velocity and average velocity equal.

Two projectiles fired with the same speed but at different angles can have the same range if the sum of their angles of projection is 90 degrees.

Uniform velocity means that the velocity of the body remains constant over time. In such a case, the average velocity over any time interval is equal to the instantaneous velocity at any point within that interval, because the velocity does not change.

Explanation

  g points down in projectile motion. Always

In a speed-time (or velocity-time) graph, the area under the graph between two points in time represents the distance traveled during that time interval. This is because the area calculation essentially sums up the product of speed and time, which is the definition of distance.

As we know average velocity depends on total displacement, and when a body reach to its initial point its displacement become zero, and Average Speed depends on distance and distance is a scaler quantity it can never be zero for a moving. object.

Explanation

For constant speed slope of the distance-time graph gives speed. In option $(a)$ slope is constant so speed is constant and in option $(c)$ velocity is constant so speed is constant.

Explanation:

The maximum range occurs when the angle of projection is 45°.

The relation between maximum height (H) and maximum range (R) for a projectile thrown at 45° is:

For uniform motion, the distance-time graph is a straight line. Because in uniform motion, the object covers equal distance in equal interval of time

2+5=7 Toward Right
and 10 N Toward Left
SO 10-7=3
so 3 N Toward Left

Note: We have to select a Direction which of one with grater magnitude 

The inertia of a body is the tendency of remaining in its static or motional state. For a heavier object, this tendency is more, and for a lighter object, it is less. Hence, the inertia is directly proportional to the mass.

For first projectile motion, the angle from horizontal is given as,

θ1​=30∘

For second projectile motion, the angle from horizontal is given as,

θ2​=90∘−30∘

=60∘
if We Sum Both θ1+θ2=90
So if the sum is 90 then Range at both angles will be the same

EXPLANATION: 

Retardation is the inverse of acceleration and is defined as a decrease in velocity per unit of time. Acceleration can be positive (+), zero (0), or negative (-). Retardation is the inverse of acceleration. Negative acceleration is also referred to as retardation or deceleration.

At the highest point of its trajectory, the projectile's velocity is entirely horizontal, while the acceleration due to gravity is vertical. These two vectors are perpendicular to each other, forming a 90-degree angle.

In motion along a straight line, the acceleration vector either points in the same direction as the velocity (when speeding up) or in the opposite direction to the velocity (when slowing down).

This is because acceleration is the rate of change of velocity, and in straight-line motion, this change can only occur along the line of motion.

in a straight line the ratio must 1:1

When a car accelerates in a straight line, its velocity increases in the direction of its motion. In this case, both the velocity and acceleration vectors point in the same direction.

This is because both projectiles are under the same constant acceleration due to gravity (assuming no air resistance). Since they experience the same gravitational force, their relative acceleration cancels out.

Therefore, the relative acceleration between the two projectiles is zero, regardless of their initial velocities.

Explanation

From first equation of motion $v=u+at$ as object starts from rest, so $u=0$ $\therefore$ $v=at$ or $v\propto t$ Therefore, $v-t$ graph is a straight line passing through 0.

Explanation:

A particle moving with a constant speed/velocity along a straight line path does not require a force to maintain its velocity.

In Newton's first law of motion, also known as the law of inertia, an object at rest will remain at rest, and an object in motion will remain in motion with a constant velocity, unless acted upon by an unbalanced force.

Since the particle is already moving with a constant velocity along a straight line path, no force is needed to maintain that motion.

One newton (N) is the force required to accelerate a mass of one kilogram (1 kg) at a rate of one meter per second squared (1 m/s²).

This is derived from Newton's second law of motion, which states that force equals mass times acceleration.

F = ma

In projectile motion, the only acceleration acting on an object is the acceleration due to gravity, which is directed vertically downward. The velocity of the object, however, can have both horizontal and vertical components. At the instant of projection, the horizontal component of velocity remains constant, while the vertical component of velocity is subject to the acceleration due to gravity and thus changes with time.

Explanation:

Velocity from a displacement–time graph = slope = Δs/Δt

But in this graph:
y-axis = time (t)
x-axis = displacement (s)

So slope = Δt/Δs = tan(30°)

tan(30°) = 1/√3

Velocity v = Δs/Δt = 1 / tan(30°) = √3 m/s

When the person pushes forward, the reaction force offered by the ice is very little. But this reaction force will help him to move forward. So, by Newton’s third law of motion, he can reach the shore

A body with a constant momentum will have a constant velocity. The momentum is defined as the product of the mass of the object and its velocity. Since the momentum is constant, that means that the product of mass and velocity is constant. So if the mass is constant and the momentum is constant then the velocity must be constant.

Note that it doesn't imply acceleration to be constant, in fact if force acts on the body and change its velocity, it must accelerate.

When velocity is uniform, velocity-time graph is straight line parallel to time axis. So, the slope is zero.

a force can cause the following effects:

1. Change in motion: A force can cause a stationary object to move or alter the velocity (speed or direction) of a moving object, as described by Newton's First Law.
2. Change in shape: A force can deform an object, either temporarily (elastic deformation) or permanently (plastic deformation).
3. Change in direction: A force can cause a moving object to change its direction without necessarily altering its speed (e.g., centripetal force).
4. Acceleration: A force can cause an object to accelerate (increase in speed), decelerate (slow down), or change its direction of motion, as per Newton's Second Law

The area under a force vs. time graph represents the impulse delivered to an object.
impulse is the change in momentum of an object it does not equal to only momentum. 

In free fall, an object is subject to the acceleration due to gravity, which is directed downward. This acceleration acts on the object regardless of whether it is on the way up or on the way down. As the velocity changes continuously and acceleration is constant, acceleration is always acting downward while it is in free fall.

According to Newton's Second Law of Motion (F = ma), force is directly proportional to acceleration. Therefore, if the force is doubled while the mass remains constant, the acceleration will also double.

Explanation

The slope of the tangent at any point on the displacement-time graph gives instantaneous velocity at that instant. In the given graph, the slope is negative at point $E$.
The velocity (v)=ds/dt​.
Therefore, instantaneous velocity at point E is negative.

As it is a about a projectile motion, the kinetic energy obviously minimum at the greatest height of the motion, but not 0. Because at the greatest height of the motion although the V(y)=0, there still exist the constant V(x) which is counted for kinetic energy.

So at the greatest height of a projectile motion, the kinetic energy of a body is minimum and the equation for this value is
K.E.= 1/2×(mv²)

At its highest point, the ball's velocity is momentarily zero. This is because it has just stopped rising due to gravity.

However, the force of gravity still acts on the ball at this point, pulling it downwards. This means the ball is still accelerating, but in the downward direction.

The acceleration due to gravity (g) is always directed downwards and has a magnitude of approximately 9.81 m/s².

Force = Mass * Acceleration

So

Acceleration = Force / Mass

= 5N / 7kg

= 0.71 m/s^2

When a person is inside a moving car and is not moving relative to the car, his speed with respect to the car is zero. This is because both the man and the car are moving with the same velocity.

Change in momentum = $m{v^{}}_2-m{v^{}}_1=-mv-mv=-2mv$

According to Newton's Third Law of Motion, every action has an equal and opposite reaction. These forces are equal in magnitude and opposite in direction, but they act on different objects, hence they do not cancel each other out on a single object.

Acceleration is the rate of change of velocity. Velocity is both an object's speed and the direction in which it is traveling, so acceleration occurs when an object changes its velocity, whether that be its speed, direction, or both.