Velocity and Acceleration Extra Credit Problem

You can also use algebraic manipulation. Are you familiar with calculus or algebraic manipulation?In summary, the conversation discusses the equation d= Vi t + 1/2at^2 and its components. It is mentioned that this equation can be shown to be true using calculus or algebraic manipulation. The variables Vi, Vf, and a are defined, and it is noted that d/t=v and v=2Vi+at/2. The conversation also includes a question about the meaning of each component of the equation.
  • #1
FreshmanInPhysics

Homework Statement


d=Vi t + 1/2at^2
What do each of these mean? Show that this is true

d=vt-Solve

v=Vf+Vi/2 - Substitute Vf with Vf= Vi+at

Homework Equations


v= average speed
Vi=initial speed
Vf= final speed

The Attempt at a Solution


Vit: This represents the initial velocity at said time elapsed
1/2at^2: This represents half the acceleration at said time elapsed squared

d/t=v

v=2Vi+at/2


 
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  • #2
FreshmanInPhysics said:

Homework Statement


d=Vi t + 1/2at^2
What do each of these mean? Show that this is true

d=vt-Solve

v=Vf+Vi/2 - Substitute Vf with Vf= Vi+at

Homework Equations


v= average speed
Vi=initial speed
Vf= final speed

The Attempt at a Solution


Vit: This represents the initial velocity at said time elapsed
1/2at^2: This represents half the acceleration at said time elapsed squared

d/t=v

v=2Vi+at/2
Welcome to the PF.

Your post is a bit jumbled. Are you in a calculus-based physics class? Calculus is one way you can show that this equation is correct.
 

FAQ: Velocity and Acceleration Extra Credit Problem

1. What is the difference between velocity and acceleration?

Velocity is the rate of change of an object's position over time, and it includes both speed and direction. Acceleration, on the other hand, is the rate of change of an object's velocity over time. In simpler terms, velocity tells us how fast an object is moving and in what direction, while acceleration tells us how quickly the velocity is changing.

2. How do you calculate velocity and acceleration?

Velocity can be calculated by dividing the change in an object's position by the change in time. Mathematically, this can be represented as v = Δx/Δt. Acceleration, on the other hand, can be calculated by dividing the change in velocity by the change in time. In formula form, this would be written as a = Δv/Δt.

3. What are the units for velocity and acceleration?

The units for velocity are typically meters per second (m/s) or kilometers per hour (km/h), depending on the scale of measurement. Acceleration is usually measured in meters per second squared (m/s^2) or kilometers per hour squared (km/h^2).

4. How does increasing velocity or acceleration affect an object's motion?

An increase in velocity will result in an object moving faster in the same direction, while a decrease in velocity will cause the object to slow down. An increase in acceleration will cause an object to change its velocity at a faster rate, resulting in a greater change in speed or direction.

5. Can velocity and acceleration be negative?

Yes, both velocity and acceleration can be negative. A negative velocity means an object is moving in the opposite direction of the reference point, while a negative acceleration means the object is slowing down. These values can also be positive, depending on the direction of motion.

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