# Determine Velocity at each second

• CollegeStudent
In summary, the conversation discusses a problem involving a ball thrown straight up at 30m/s with an acceleration of 10m/s/s. The displacement, velocity, and acceleration at each position are calculated using the equations Vf = Vi + at and Vf² = Vi² + 2aΔx. The velocity is determined by tabulating Vf = Vi + a*t and using the results in the first equation. The resulting accelerations depend on the chosen sign convention for velocities, with positive velocities resulting in positive acceleration and vice versa.
CollegeStudent

## Homework Statement

A ball is thrown straight up at 30m/s. Assume g is 10m/s/s Show the dispacement, velocity, and acceleration at each position.

Vf² = Vi² + 2aΔx
Vf = Vi + at

## The Attempt at a Solution

So first I wanted to solve for the time it takes to go up so

Vf = Vi + at
0 = 30 + (-10)t
t = -30/-10 = 3 seconds up
then just times 2 because its the same coming down
so 6 seconds in all

Now for distance up

Vf² = Vi² + 2aΔx
Δx = (Vf² - Vi²)/2a
Δx = (0 - 900)/2(-10)
Δx = (-900)/(-20)
Δx = 45m up
and again times 2
so 90 meters in all

Now for some reason I'm having trouble figuring out how to find the velocity,displacement,and acceleration at each 1 second interval.

Should acceleration stay the same until the top where its 0 then change to +10m/s/s?

And how and what formula would I use for the other two?

Hint: For the velocity simply tabulate Vf = Vi + a*t. On the way up, a is negative. Use results for Vf in your first equation and solve for delta X. Repeat.

Thanks Lawrence ...I kept thinking I had to bring in another formula. Thanks again!

Actually ...when solving for acceleration ...I get that on the way up its negative ...but by using something using my results from above...
Vf = Vi + at
(Vf-Vi)/t

Using say
V(0)=30m/s and V(1)=20m/s
So
(20-30)/1 = -10 which I assumed

But

Using V(4) and V(5)

(-20 - (-10))/1
That comes to -10 as well...but shouldn't acceleration be positive at this time?

If you choose the starting point to be the velocity at the highest point where it is zero and let downward velocities be positive, then you will get a positive acceleration.

The equation Vf = Vi + at enables one to determine a velocity at a later time under constant acceleration over that time period. If the acceleration is in the same direction as the velocity and velocity is positive, acceleration is positive. Vice versa is also true. If you use it to determine accelerations, the sign of the acceleration is dependent on the sign convention you choose for the velocities. If the magnitude of the velocity increases, the acceleration has the same sign as the velocity. If magnitude of velocity decreases, acceleration has the opposite sign.

## 1. What is velocity?

Velocity is a measure of an object's speed and direction. It tells us how fast an object is moving in a specific direction.

## 2. How is velocity calculated?

Velocity is calculated by dividing the change in an object's position by the change in time. This is also known as the slope of the position-time graph.

## 3. What are the units of velocity?

The units of velocity are distance over time, such as meters per second (m/s) or kilometers per hour (km/h).

## 4. Can velocity be negative?

Yes, velocity can be negative if the object is moving in the opposite direction of the chosen positive direction. This is known as a negative velocity or a velocity with a negative sign.

## 5. How can velocity change over time?

Velocity can change over time if there is a change in the object's speed or direction. This can be due to factors such as acceleration, deceleration, or changes in the object's path.

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