Speed And Velocity

The correct option is (A). The velocity-time graph for a body that starts from rest and moves with a constant acceleration is a straight line that passes through the origin. The graph shows a linear relationship between velocity and time, indicating constant acceleration.

The stopping distance of a moving vehicle is related to the initial velocity by the work-energy principle. The kinetic energy of the vehicle is given by:

Where: - is the mass of the vehicle, - is the initial velocity. The work done by the braking force is equal to the kinetic energy, and the stopping distance is related to the work done by the formula: Assuming that the braking force is constant, we can solve for the stopping distance : Since the braking force is constant, we can conclude that the stopping distance is proportional to the square of the initial velocity . Thus, the correct relationship is: Therefore, the stopping distance is proportional to the square of the initial velocity.

Correct Answer:

Correct Answer: (D) square of the initial velocity

The hammer is dropped into a mine, and we are asked to find the ratio of its velocities at different depths , , and .

When an object is in free fall, its velocity at any point is given by the equation: Where: - is the velocity, - is the acceleration due to gravity, - is the height or depth from the point of release. Now, at depths , , and , the velocities are: - At depth : - At depth : - At depth : The ratio of velocities at these depths is: Simplifying the ratio: This shows that the velocities at depths , , and are in the ratio 1:2:√3

Correct Answer:

Correct Answer: (E) 1:2:√3

The velocity of a particle is given as , which means the velocity vector has components of 1 unit in both the -direction and -direction. So the velocity vector is:

The magnitude of the velocity vector is given by the formula for the magnitude of a vector: So, the magnitude of the velocity is units. The direction of the velocity vector is given by the angle it makes with the -axis. The angle can be calculated using the formula: Thus, Therefore, the magnitude of the velocity is units and the direction is with respect to the -axis.

Correct Answer:

Correct Answer: (A) units and 45° with the x-axis

We are given that when a physical quantity A is multiplied with velocity, the resulting quantity is B, and we are told that B is energy. Our task is to determine what A is.

Energy ( ) is related to momentum ( ) and velocity ( ) by the equation:

Where: - is energy, - is momentum, - is velocity. From this equation, we can deduce that A must be momentum, as multiplying momentum with velocity results in energy.

The correct answer is momentum.

Correct Answer:

Correct Answer: (B) momentum