Finding Velocity and Position of a Moving Particle: A Function of Time

In summary, the conversation is about finding the velocity and equation of a particle moving along an x-axis with constant velocity. The first part involves finding the velocity by dividing the time interval by displacement. The second part focuses on finding the equation that expresses x as a function of t, with the constant of proportionality being the velocity. The correct equation is x=2t-3 and the position at time t=0 is x=-3.
  • #1
Loppyfoot
194
0

Homework Statement


A particle moving along an x-axis with constant velocity is at the point x=1 when t=2 and is at the point x=5 when t=4. Find the velocity of the particle if x is in meters and t is in seconds. Find an equation that expresses x as a function of t.


Homework Equations





The Attempt at a Solution


I got the first part. (4-2)/(5-1) = 0.5m/s. Now, how do I get the equation that expresses x as a function of t?
 
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  • #2
You got the first part by assuming that the object covers equal distances in equal times. Can you write an equation that expresses that?

** Edit **

Actually you did not get the first part. You divided time interval by displacement.
 
Last edited:
  • #3
Oh, so would the velocity be 2?
Ok, so x=2t+?
So, it is 2t-3.
Right?
 
Last edited:
  • #4
Yes, x is directly proportional to time, the constant of proportionality being the velocity. To find the velocity, you need to do part (a) correctly. The y intercept in this case is the position of the particle at time t = 0.
 
  • #5
So when time = 0, the particle is at coordinate x=-3.
 
  • #6
You got it.
 
  • #7
Thanks for notifying me of my mistake!
 

1. What is velocity?

Velocity is a measure of an object's speed and direction of motion. It is a vector quantity, meaning it has both magnitude (speed) and direction (positive or negative). The unit of velocity is meters per second (m/s) in the International System of Units (SI).

2. How is velocity different from speed?

Velocity and speed are often used interchangeably, but they are not the same. While speed only refers to the rate of motion, velocity also takes into account the direction of motion. For example, if a car is traveling at a speed of 60 mph in a northward direction, its velocity would be 60 mph north.

3. What is the relationship between velocity and acceleration?

Acceleration is the rate at which an object's velocity changes over time. In other words, it is the change in velocity divided by the change in time. The direction of acceleration is determined by the direction of the change in velocity. If an object's velocity is increasing, its acceleration is positive. If its velocity is decreasing, its acceleration is negative.

4. How are position, velocity, and time related?

Position, velocity, and time are all important factors in describing an object's motion. Position refers to the location of an object in space, velocity describes how fast and in what direction an object is moving, and time measures the duration of the motion. Together, these quantities can be used to calculate an object's displacement (change in position) and its average velocity.

5. Can an object have a constant velocity and changing position?

No, if an object has a constant velocity, it means it is moving at a constant speed in a constant direction. This would result in a straight-line motion. If an object's position is changing, its velocity must also be changing, either in speed, direction, or both.

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