Tracking a Particle's Motion Along x-Axis

In summary, the particle's position on the x-axis can be calculated using the equation x = 1.92 + 3.09t − 1.00t2, where x is in meters and t is in seconds. Using this equation, the position of the particle at t=3.4s is 0.866m. To find the velocity and acceleration at t=3.4s, calculus is needed to take the derivative. For further assistance, referring to a calculus textbook or asking a professor is recommended.
  • #1
jnunes5707
3
0
A particle moves along the x-axis according to the equation:

x = 1.92 + 3.09t − 1.00t2,
Where x is in meters and t is in seconds?


a) find the position of the particle at t=3.4s
-I get this part. (0.866m)

b) find its velocity at t=3.4s
-this is where I am having trouble. I know I need to use calculus to take the derivative, but my physics class is actually ahead of my cal 1 class so I'm struggling a bit trying to conceptualize how to plug this into the derivative definition.

c) find its acceleration at t=3.4s

I know its a basic problem, and you guys probably see this a lot, but I appreciate your feedback.
 
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  • #2


Go look up how to do derivatives in your calculus textbook or ask your professor.
 

1. What is the x-axis?

The x-axis is a horizontal line on a graph that represents the independent variable in a scientific experiment. It is typically labeled as the "x" or "horizontal" axis and is used to plot the values of the variable being studied.

2. How do you track a particle's motion along the x-axis?

To track a particle's motion along the x-axis, you will need to use a position-time graph or an x-t graph. This graph plots the particle's position (x) on the y-axis and time (t) on the x-axis. By analyzing the slope of the graph, you can determine the particle's velocity and acceleration along the x-axis.

3. What is the difference between displacement and distance traveled along the x-axis?

Displacement is a vector quantity that refers to the change in position of a particle along the x-axis, while distance traveled is a scalar quantity that refers to the total length of the path traveled by the particle along the x-axis. Displacement can be positive or negative, while distance traveled is always positive.

4. What is the relationship between velocity and acceleration along the x-axis?

Velocity and acceleration are both vector quantities that describe the motion of a particle along the x-axis. Velocity is the rate of change in position of the particle, while acceleration is the rate of change in velocity. Therefore, acceleration is the derivative of velocity with respect to time along the x-axis.

5. How can you use a velocity-time graph to track a particle's motion along the x-axis?

A velocity-time graph, also known as a v-t graph, plots the velocity of a particle on the y-axis and time on the x-axis. By analyzing the slope of this graph, you can determine the particle's acceleration along the x-axis. Additionally, the area under the curve on a v-t graph represents the displacement of the particle along the x-axis.

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