A 0.38-kg particle has a speed of 2.0 m/s at point A and kinetic energy of 7.5 J at point B.

(a) What is its kinetic energy at A?
J

(b) What is its speed at point B?
m/s

(c) What is the total work done on the particle as it moves from A to B?

a,b) KE= 1/2 mass*v^2

c) the work done is the difference in energies at A,B

To solve this problem, we can use the formula for kinetic energy:

Kinetic energy = (1/2) * mass * speed^2

Let's calculate the answers step by step.

(a) What is its kinetic energy at A?

Given:
Mass (m) = 0.38 kg
Speed at point A (v_A) = 2.0 m/s

To find the kinetic energy at A, we can use the formula for kinetic energy:

Kinetic energy at A = (1/2) * mass * speed^2

Substituting the given values:

Kinetic energy at A = (1/2) * 0.38 kg * (2.0 m/s)^2

Kinetic energy at A = 0.38 * 2.0^2 J

Kinetic energy at A = 0.38 * 4.0 J

Kinetic energy at A = 1.52 J

Therefore, the kinetic energy at point A is 1.52 J.

(b) What is its speed at point B?

Given:
Mass (m) = 0.38 kg
Kinetic energy at point B (K_B) = 7.5 J

To find the speed at point B, we need to rearrange the formula for kinetic energy:

Kinetic energy = (1/2) * mass * speed^2

Solving for speed:

speed = √(2 * kinetic energy / mass)

Substituting the given values:

speed at B = √(2 * 7.5 J / 0.38 kg)

speed at B = √(15 J / 0.38 kg)

speed at B = √(39.47 m^2/s^2)

speed at B ≈ 6.28 m/s

Therefore, the speed at point B is approximately 6.28 m/s.

(c) What is the total work done on the particle as it moves from A to B?

The work done on a particle is given by the change in its kinetic energy.

Change in kinetic energy = Kinetic energy at B - Kinetic energy at A

Substituting the given values:

Change in kinetic energy = 7.5 J - 1.52 J

Change in kinetic energy = 5.98 J

Therefore, the total work done on the particle as it moves from point A to point B is 5.98 J.

To solve this problem, we need to use the formulas for kinetic energy and work done.

(a) To find the kinetic energy at point A, we can use the formula:

Kinetic Energy = 1/2 * mass * velocity^2

Given that the mass of the particle is 0.38 kg and the speed at point A is 2.0 m/s, we can substitute these values into the formula:

Kinetic Energy at A = 1/2 * 0.38 kg * (2.0 m/s)^2

Simplifying this equation:

Kinetic Energy at A = 1/2 * 0.38 kg * 4.0 m^2/s^2

Kinetic Energy at A = 0.38 kg * 2.0 m^2/s^2

Kinetic Energy at A = 0.76 J

So, the kinetic energy at point A is 0.76 J.

(b) To find the speed at point B, we need to rearrange the kinetic energy formula and solve for velocity:

Kinetic Energy = 1/2 * mass * velocity^2

Substituting the given values, we have:

7.5 J = 1/2 * 0.38 kg * velocity^2

Rearranging the equation:

velocity^2 = (7.5 J * 2) / (0.38 kg)

velocity^2 = 39.47 m^2/s^2

Taking the square root of both sides to solve for velocity:

velocity = √(39.47 m^2/s^2)

velocity ≈ 6.28 m/s

So, the speed at point B is approximately 6.28 m/s.

(c) The work done on the particle as it moves from point A to point B is given by the change in kinetic energy. We can calculate it using the formula:

Work = Kinetic Energy at B - Kinetic Energy at A

Substituting the values we found earlier:

Work = 7.5 J - 0.76 J

Work = 6.74 J

So, the total work done on the particle as it moves from A to B is 6.74 J.