Proof of constant acceleration

In summary, a proton has a constant acceleration, a, equal to the cross product of the velocity, v, and the constant magnetic field, B, multiplied by a constant, C. To prove that the magnitudes of v and a are constant, we can use the fact that the scalar product of acceleration and velocity must be zero, as the acceleration is perpendicular to the velocity in this case. This means that no work is being done and the kinetic energy remains constant. This also proves that the magnitudes of v and a are constant.
  • #1
subwaybusker
51
0
A proton has the acceleration a=CvxB, where a is the cross product of v and B (a,v,B are vectors). C is a constant and the magnetic field is constant. Prove that the magnitude of the v and a are constant.

I know I have to somehow prove the derivative of a or v to be zero, but i have no idea how to start. i know if v is constant, then a must be 0.

a=CvxB
(da/dt)=C(dv/dt)xB

i also wrote down |a|=|Cv||B|sintheta, but that doesn't help at all.
 
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  • #2
If the acceleration is the vector product of the velocity and something else, the acceleration is at right angles to the velocity. The scalar product of acceleration and velocity must then be zero. (The scalar product of two vectors is the product of their magnitudes and the cosine of the angle between them. Cosine of 90 degrees is zero.) But this scalar product is the power per kilogram (work per kilogram per second) delivered by the force.

The derivative to time of the velocity is not zero; it is the acceleration. But it merely changes the direction of the velocity in this case, not its magnitude. So the kinetic energy does not change, and no work is done.
 
  • #3
solved it, thanks!
 
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1. What is "Proof of constant acceleration"?

"Proof of constant acceleration" refers to the evidence or demonstration that an object is experiencing a steady rate of change in its velocity over time.

2. How is constant acceleration different from regular acceleration?

Constant acceleration means that the rate of change in velocity is consistent and does not vary over time, while regular acceleration can vary in magnitude and direction.

3. What is the formula for calculating constant acceleration?

The formula for calculating constant acceleration is a = (v - u) / t, where a is acceleration, v is final velocity, u is initial velocity, and t is time.

4. What are some real-world examples of constant acceleration?

Some real-world examples of constant acceleration include objects falling due to gravity, a car accelerating at a constant rate on a straight road, and a rocket launching into space.

5. How is constant acceleration used in scientific research?

Constant acceleration is used in scientific research to study the motion of objects in various scenarios and to make predictions about their future movement. It can also be used to test the effects of different forces on an object's acceleration.

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