# 2 dimensional motion - calculate particles position

• new^2^physics
In summary, the particle starts from rest at x=0 and accelerates at a rate of +2.0 cm/s2 for 10 seconds, after which it decelerates at a rate of -1.0 cm/s2 for 20 seconds. The total distance traveled is +3.0 m, making choice b the correct answer.
new^2^physics

## Homework Statement

A particle starts from rest x=0 and moves for 10 s with an acceleration component of +2.0 cm/s2. for the next 20 s, the acceleration component of the particle is -1.0 cm/s2. What is the position of the particle at the end of this motion?

a. zero
b. + 3.0 m
c. - 1.0 m
d. +2.0 m
e. -3.0 m

2. The attempt at a solution

a. deltaX = Vit + 1/2 At2
= 0 (10) + 1/2 (0.02)(102)
= 1m

b. velocity
vf = vi +at
= 0 + (0.02)(10)
= 0.2 m/s

c. deltaX = Vit + 1/2 At2
= (0.2)(20) = 1/2 (-0.01)(202)
= 2m

d. total distance traveled is 1m + 2m = + 3.0m

Therefore I would argue that "b" would be the correct answer. Is this correct?

Looks correct to me.

## 1. How do you calculate the position of a particle in 2 dimensional motion?

To calculate the position of a particle in 2 dimensional motion, you will need to use the equations for displacement, velocity, and acceleration. First, determine the initial position of the particle and its velocity. Then, use the equation x = x0 + v0t + 1/2at2 to calculate the position at a specific time t.

## 2. What is the difference between displacement and distance in 2 dimensional motion calculations?

In 2 dimensional motion, displacement refers to the change in position of a particle from its initial position to its final position, taking into account both the magnitude and direction. Distance, on the other hand, refers to the total length of the path traveled by the particle.

## 3. Can you use the equations for 2 dimensional motion to calculate the position of a particle at any time?

Yes, the equations for 2 dimensional motion can be used to calculate the position of a particle at any time, as long as you have the necessary information such as the initial position, velocity, and acceleration. Just plug in the values into the equation x = x0 + v0t + 1/2at2 and solve for x.

## 4. How does acceleration affect the position of a particle in 2 dimensional motion?

Acceleration affects the position of a particle in 2 dimensional motion by changing its velocity. If the acceleration is in the same direction as the particle's initial velocity, it will speed up the particle and cause it to travel a greater distance in a shorter amount of time. However, if the acceleration is in the opposite direction, it will slow down the particle and cause it to travel a shorter distance in a longer amount of time.

## 5. What is the difference between average velocity and instantaneous velocity in 2 dimensional motion?

Average velocity in 2 dimensional motion is the overall change in position of a particle over a specific time interval. It is calculated by dividing the change in position (displacement) by the change in time. Instantaneous velocity, on the other hand, refers to the velocity of the particle at a specific moment in time. It is calculated by taking the derivative of the position function with respect to time.

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