# Writing Equations for Position, Velocity, and Accelerations as functions of time

• Jordash
In summary, the conversation discusses a projectile motion problem where a projectile is launched from a cliff onto a flat valley floor. The equations for position, velocity, and acceleration as functions of time are requested for this problem, with the assumption of constant gravity and no aerodynamic effects. The concept of a projectile and the use of kinematics formulas for constant acceleration are also mentioned.
Jordash

## Homework Statement

A projectile is launched with a speed of 50.0 m/s and an angle of 40.0o above the horizontal, from the top of a 75.0 m high cliﬀ onto a ﬂat valley ﬂoor at the base of the cliﬀ. Assume that g = 10.0 m/s2 and ignore aerodynamic eﬀects.

Write equations for position, velocity, and acceleration as function of time for the projectile.

## The Attempt at a Solution

I've been looking through the time functions but I can't seem to figure out how to write these equations. Any help would be greatly appreciated.

It's a projectile motion problem. What is a projectile? An object that, once set into motion (launched) travels solely under the influence of gravity. Gravity is a constant force (it isn't really, but it is for our purposes, unless you're traveling really large vertical distances). So you already know that the acceleration is constant (doesn't change with time). From that you can either work backwards using calculus to find the velocity and position. OR, if you haven't studied calculus, then your teacher will have taught you kinematics formulas that *describe* the motion of an object under constant acceleration (formulas that are derived from calculus), and you can just *use* them.

I didn't really understand our teacher when he taught those formulas, is there a place I can look which teaches the formulas i'll need to use?

accident put wrong post in this forum

Last edited:

## 1. What is the difference between position, velocity, and acceleration?

Position refers to an object's location in space, velocity refers to the rate of change of an object's position, and acceleration refers to the rate of change of an object's velocity. In other words, position is where the object is, velocity is how fast the object is moving, and acceleration is how much the object's speed is changing.

## 2. How do I write an equation for position as a function of time?

The equation for position as a function of time is x(t) = x0 + v0t + ½at2, where x0 is the initial position, v0 is the initial velocity, a is the acceleration, and t is time. This equation can be used to calculate an object's position at any given time if its initial position, initial velocity, and acceleration are known.

## 3. How do I write an equation for velocity as a function of time?

The equation for velocity as a function of time is v(t) = v0 + at, where v0 is the initial velocity, a is the acceleration, and t is time. This equation can be used to calculate an object's velocity at any given time if its initial velocity and acceleration are known.

## 4. How do I write an equation for acceleration as a function of time?

The equation for acceleration as a function of time is a(t) = a0, where a0 is the initial acceleration. This equation assumes that the acceleration is constant over time. If the acceleration is not constant, a more complex equation must be used.

## 5. Can I use these equations for objects moving in a circular motion?

Yes, these equations can be used for objects moving in a circular motion, but additional equations may be needed to account for the direction of the velocity and acceleration. For example, the equation for velocity in circular motion is v(t) = ωr, where ω is the angular velocity and r is the radius of the circular path. The equations for position and acceleration may also differ depending on the specific scenario of the circular motion.

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