Is velocity the same as acceleration?

Question

I am asked to find the maximum velocity of a mass.

I know that the equation for maximum acceleration is

$$a = w^2A$$

However I do not know how to find the maximum velocity. Is velocity just the same as acceleration?

Answer 1

Velocity is the rate of change of position. It's pretty much just the speed of the object, with a little extra structure to keep track of the direction it's moving.

Acceleration is the rate of change of the velocity. It incorporates both the object speeding up and slowing down, and the object turning to move in a different direction.

Now, from the form of the acceleration equation you gave, I'm guessing this is a mass on a spring problem. In that case, the maximum velocity can be found from either differentiating the mass's position function (which should be $x = A\sin(\omega t + \phi)$) or from conservation of energy ($m\omega^2x^2/2 + mv^2/2= m\omega^2A^2/2$).

Answer 2

Velocity is not the same as acceleration. Acceleration is a measure of how your velocity changes over time: speed up, and acceleration is positive, etc. This is similar to how velocity measures how your position changes over time. Indeed, velocity is the derivative of position, and acceleration is the derivative of velocity.

Here's a hint for the problem: when velocity is maximal, what do you think the acceleration is going to be?

Answer 3

If the position is given by $x = x(t)$ then the velocity is $v = \dot{x}$ and the acceleration $a = \dot{v} = \ddot{x}$. The dot is the Newton-style notation for the derivative regarding time.

Answer 4

acceleration depends on the applied force and the mass

acceleration = force/mass

for uniform acceleration velocity = acceleration X time

if acceleration varies you must integrate to find velocity = integral of acceleration over time