Velocity and Acceleration of a particle

In summary, the problem involves finding the position, velocity, and acceleration of a particle with given coordinates. To find the acceleration, the derivative of the velocity components must be taken. The time at which the velocity's horizontal and vertical components are equal can be found by setting the position functions equal and solving for time.
  • #1
cougar_21
15
0
Velocity and Acceleration Please Help!

My problem reads:

A particle is observed to move with the coordinates x(t)=(1.5m/s)t + (-0.5 m/s^2)t^2 and y(t) = 6m + (-3m/s)t + (1.5 m/s^2)t^2. What are the particle's position, velocity, and acceleration? At what time(s) are the velocity's horizontal and vertical components equal?

I got the derivative of x(t) and y(t) to get v(x) and v(y). Where do I go from there :confused:
 
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  • #2
do get the acceleration take the derivative of V(x) and V(y).

For the what time thing, set them equal, solve for "t"?
 
  • #3
For the second question, solve for x(t) = y(t).
 

1. What is the difference between velocity and acceleration?

Velocity is the rate of change of an object's displacement with respect to time, while acceleration is the rate of change of an object's velocity with respect to time. In simpler terms, velocity measures how fast an object is moving, while acceleration measures how quickly the velocity is changing.

2. How are velocity and acceleration related?

Velocity and acceleration are related through the concept of derivatives. Acceleration is the derivative of velocity, meaning it is the rate of change of velocity with respect to time. This means that the acceleration of an object can be found by taking the derivative of its velocity function.

3. How do you calculate velocity and acceleration?

Velocity can be calculated by dividing the change in position of an object by the change in time. Mathematically, this can be represented as v = Δx/Δt. Acceleration can be calculated by dividing the change in velocity by the change in time, or by taking the second derivative of an object's position function.

4. What is the difference between average velocity and instantaneous velocity?

Average velocity is the total displacement of an object divided by the total time taken, while instantaneous velocity is the velocity of an object at a specific moment in time. Average velocity gives an overall picture of an object's motion, while instantaneous velocity provides information about its motion at a specific point in time.

5. How does acceleration affect an object's motion?

Acceleration directly affects an object's motion by changing its velocity. If an object is accelerating, its velocity will either increase or decrease depending on the direction of the acceleration. This means that the object's position will change at a faster or slower rate, ultimately affecting its overall motion.

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