# Speed with constant acceleration

• ahuebel
In summary, the conversation discusses the use of a Newton equation for position and the resulting formula for speed. The formula v^2= v0^2+2a(x-x0) is for uniformly accelerated straight-line motion and can be used to solve for any of the variables. While some may find it confusing, the use of v^2 rather than v in the equation is simply a matter of preference.
ahuebel
Using a Newton equation for position and substituting (v-v0)/a for t you can get the following formula:
v^2= v0^2+2a(x-x0) where v^2 is supposedly speed. I understood speed to be tha magnitude of velocity which is the sqrt of the sum of the squares of the components (i.e. sqrt(vx^2+vy^2+vz^2)). I seem to be missing something... how is speed then v^2? I am sure it is right in front of my face but I am just not seeing it.

TIA

v^2 is the speed squared; v is the speed.

Realize that your formula ,v^2= v0^2+2a(x-x0), is for uniformly accelerated straight-line motion.

Thank you. It just seems odd that if they would state that an equation is speed as a fucnction of position it would be much better to have that equation be v = sqrt(v0^2+2a(x-x0)). It can throw simple people like me off :).

Think of that equation as a relationship among all the different variables, not just as a formula for finding speed. Depending upon what information is given, you may wish to use it to solve for any of the variables. (And having a single v^2 is much nicer looking than that ugly square root! )

## 1. What is speed with constant acceleration?

Speed with constant acceleration is the rate at which an object's velocity changes over time, while the acceleration remains constant. It is calculated by multiplying the acceleration by the time interval and adding it to the initial velocity.

## 2. How is speed with constant acceleration different from average speed?

Speed with constant acceleration is different from average speed because it takes into account the changing velocity of an object over time, while average speed only considers the total distance travelled divided by the total time taken.

## 3. What is the formula for calculating speed with constant acceleration?

The formula for calculating speed with constant acceleration is v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time interval.

## 4. Can an object have a constant acceleration and changing speed?

Yes, an object can have a constant acceleration and changing speed if the acceleration is not in the same direction as the velocity. This is known as non-uniform acceleration.

## 5. How does air resistance affect speed with constant acceleration?

Air resistance can decrease the speed of an object with constant acceleration because it acts as a force in the opposite direction of motion, slowing the object down. This is known as drag and can significantly affect the speed of objects moving through air or other fluids.

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