Velocity of a mass m that moves along the x-axis

Thread starter lily
Start date Oct 17, 2021
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Calc 1 Mass Velocity

In summary, velocity is a vector quantity that measures the rate and direction of an object's motion. It is calculated by dividing the change in an object's position by the change in time. While often used interchangeably, velocity and speed have distinct definitions in physics. Velocity can be negative, indicating motion in the opposite direction of the positive x-axis. Mass does not directly affect velocity but can influence an object's acceleration, ultimately impacting its velocity.

Oct 17, 2021

lily

Homework Statement: A particle of constant mass m moves along the x-axis. Its velocity v and position x satisfy the equation: 1/2m(v^2 - v0^2) = 1/2k(x0^2-x^2), where k, v0 and x0 are constants. Show that whenever v does not equal 0, mdv/dt=-kx.

Relevant Equations: 1/2m(v^2 - v0^2) = 1/2k(x0^2-x^2)

mdv/dt=-kx.

dv/dt(mv^2-mv0^2) = dv/dt(kx0^2-kx^2)

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Oct 17, 2021

anuttarasammyak

Gold Member

lily said:

Relevant Equations:: 1/2m(v^2 - v0^2) = 1/2k(x0^2-x^2)

Differentiate the both hand sides by time i.e. d/dt

Related to Velocity of a mass m that moves along the x-axis

1. What is velocity?

Velocity is a measure of the rate at which an object changes its position. It is a vector quantity that includes both magnitude (speed) and direction.

2. How is velocity calculated?

Velocity is calculated by dividing the change in position (displacement) by the change in time. Mathematically, it can be expressed as v = Δx/Δt, where v is velocity, Δx is change in position, and Δt is change in time.

3. What is the difference between velocity and speed?

Velocity and speed are often used interchangeably, but they are actually different concepts. While velocity includes the direction of motion, speed only measures the magnitude of motion.

4. How does mass affect velocity?

Mass does not directly affect velocity. However, a larger mass may require more force to accelerate to a certain velocity, while a smaller mass may require less force.

5. Can velocity be negative?

Yes, velocity can be negative. A negative velocity indicates that the object is moving in the opposite direction of the positive direction on the x-axis.