Solving for Velocity: 8.2 kg Object Moving Along x-Axis

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In summary, an 8.2 kg object is moving in the positive direction of an x axis and when it passes through x = 0, a constant force begins to act on it. The object's kinetic energy at x = 0 is 27.5 J and its velocity is 3.6 m/s. As it continues to move in the negative direction, its kinetic energy increases to 55 J at x = 5.0 m, resulting in a velocity of 4.3 m/s when it moves back through x = -3.0 m. The equations used to solve for the velocity at each point were K = 1/2mv^2 and v = sqrt((K - 27.5
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Homework Statement



An 8.2 kg object is moving in the positive direction of an x axis. When it passes through x = 0, a constant force directed along the axis begins to act on it. The figure below gives its kinetic energy K versus position x as it moves from x = 0 to x= 5.0 m; K0 = 27.5 J. The force continues to act. What is v when the object moves back through x = -3.0 m?

Homework Equations





The Attempt at a Solution


 
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When the object passes through x = 0, its kinetic energy is 27.5 J. We can use the equation K = 1/2mv^2 to solve for v at x = 0: 27.5 J = (1/2)(8.2 kg)(v^2)v = sqrt(54.5 J/8.2 kg)v = 3.6 m/sSince the force continues to act on the object as it moves in the negative direction, the object's kinetic energy will increase. When the object passes through x = -3.0 m, we can again use the equation K = 1/2mv^2: K = 27.5 J + mv^2 K = 27.5 J + (8.2 kg)(v^2)27.5 J + (8.2 kg)(v^2) = K (8.2 kg)(v^2) = K - 27.5 J v = sqrt((K - 27.5 J)/(8.2 kg)) We know that K = 55 J when the object is at x = 5.0 m, so: v = sqrt((55 J - 27.5 J)/(8.2 kg)) v = sqrt(27.5 J/8.2 kg) v = 4.3 m/s
 

1. What is velocity?

Velocity is a measure of an object's speed and direction of motion. It is a vector quantity, meaning it has both magnitude (speed) and direction.

2. How is velocity calculated?

Velocity is calculated by dividing the change in an object's position by the change in time. It can be represented by the equation v = Δx/Δt, where v is velocity, Δx is the change in position, and Δt is the change in time.

3. What is the unit of velocity?

The unit of velocity depends on the unit of distance and time used in the calculation. In the metric system, velocity is typically measured in meters per second (m/s). In the imperial system, it is measured in feet per second (ft/s) or miles per hour (mph).

4. How is velocity affected by mass?

In the absence of external forces, the velocity of an object is not affected by its mass. This is known as the principle of inertia, which states that an object will maintain its state of motion unless acted upon by a net external force.

5. How does velocity change in different directions?

Velocity can change in magnitude and direction depending on the forces acting on an object. For example, if an object is moving along the x-axis and a force acts on it in the y-direction, the velocity will change in both magnitude and direction according to the net force applied.

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