# Acceleration of object and displacement after given time

• princesspriya
In summary: One for the direction it starts off going in and another for the direction it ends up going in.In summary, a kitten displaces a ball of yarn by pushing it at 1.00 cm/s with its nose, causing the ball of yarn to move in the opposite direction at a final velocity of 16.5 cm/s in 2.00 s. Using the equations x = (vi)t + 1/2 (a)(t^2) and vf = vi + at, a student calculated the acceleration of the ball of yarn to be 7.75 m/s^2. However, their teacher marked it wrong due to not choosing a consistent coordinate system for direction.

## Homework Statement

a kitten pushes a ball of yarn rolling toward it at 1.00 cm/s with its nose, displacing the ball of yarn 17.5 cm in the opposite direction in 2.00 s. What is the acceleration of the ball of yarn?

## The Attempt at a Solution

i used x=1/2(Vi+Vf)t to find the final velocity and i got 16.5.
than i used the vf=vi+at and got 7.75m/s^2 for the acceleration but my teacher told me its wrong so i have no clue like what i did wrong?

I would just use x = (vi)t + 1/2 (a)(t^2)

and remember that vi is -1.

y would vi be negative? it just says opposite its not saying east or west so you really cannot tell

You just need to know that the ball is moving in one direction to start with, and then ends up moving in a different direction. So you assign the direction it ends up going as being positive and the direction it was going at the start as being negative.

princesspriya said:
y would vi be negative? it just says opposite its not saying east or west so you really cannot tell

You get to choose. Lamoid is recommending a coordinate system in which velocities and displacements in the direction towards the cat are negative and velocities and directions away from it are positive, by definition. It doesn't matter if you choose things to be the other way around. But you have to pick a coordinate system and stick with it consistently throughout the problem, because velocities and displacements have both magnitude and direction, so you need some way to distinguish between motion in one direction and motion in the opposite direction.

so then if i picked to the east than everything would be positive correct? and i think my answer is correct since Vi=1 T=2 and X=17.5 but i mean he marked it wrong so i really am lost now

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princesspriya said:
so then if i picked to the east than everything would be positive correct? and i think my answer is correct but i mean he marked it wrong so i really am lost now

Huh? No. This is a one-dimensional problem. Hence, the ball can either be moving THIS way, or THAT way (there are two possible directions along the axis). Clearly at the beginning of the problem the ball is moving in ONE direction (which you have the choice of calling negative or positive), and by the end of the problem, the ball has changed direction and is moving in OTHER direction (for which you must use the opposite sign from whatever sign you used for the initial direction, in order to distinguish the two). You need two signs.

## What is acceleration?

Acceleration is the rate at which an object changes its velocity over time. It is a vector quantity, meaning it has both magnitude and direction.

## How is acceleration calculated?

Acceleration can be calculated by dividing the change in velocity by the change in time. The formula for acceleration is a = (vf - vi) / t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

## What is the difference between acceleration and velocity?

Velocity is the rate of change of an object's displacement over time, while acceleration is the rate of change of an object's velocity over time. In other words, velocity tells us how fast an object is moving, while acceleration tells us how quickly its velocity is changing.

## How does acceleration affect displacement?

Acceleration can affect an object's displacement by changing its velocity. The greater the acceleration, the more an object's velocity will change over time, which can result in a greater displacement. However, if the acceleration is constant, the displacement can be calculated using the formula d = v0t + (1/2)at^2, where d is displacement, v0 is initial velocity, t is time, and a is acceleration.

## What factors can affect the acceleration of an object?

The acceleration of an object can be affected by various factors, including the force applied to the object, its mass, and any external factors such as friction or air resistance. The direction of the applied force also plays a role in determining the acceleration of an object.