Calculate objects Position/acceleration as function of time

So you can find the position and acceleration functions by just taking derivatives of the given function for vx(t). In summary, to calculate the position and acceleration of an object as a function of time using the given equation vx(t)=a-bt^2, you can take the derivatives of the equation to find the functions for x(t) and a(t). Additionally, the maximum positive displacement from the origin can be found by using the equation V2^2= V1^2 + 2aD and substituting in the values for V1 and a.
  • #1
anubis01
149
1

Homework Statement


vx(t)=a-bt^2
a=4.0 m/s
b=2.0 m/s^2
At t=0 the object is at x=0

a)Calculate objects position as a function of time
b)Calculate objects acceleration as a function of time
c)What is objects maximium positive displacement from the origin


Homework Equations


vx(t)=a-bt^2


The Attempt at a Solution


a)Xf=x1 + V1t + 1/2at^2
Xf=0 + 4(0)+1/2(9.8)(0)^2

c)V2^2= V1^2 + 2aD
-V1^2/2a)=D
-16/-4=4

I'm particularly stumped on question a & b because I'm not quite sure what ithe question is asking and I'm not entirly confident that C is correct. Any help is appreciated.
 
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  • #2
You could use the fact that velocity is just the derivative of displacement with respect to time, and then for (b) just recognize that acceleration is the derivative of velocity.
 
  • #3


a) To calculate the object's position as a function of time, you can use the equation x(t) = x0 + v0t + 1/2at^2, where x0 is the initial position and v0 is the initial velocity. In this case, x0 = 0 and v0 = 4 m/s. So the equation becomes x(t) = 4t - t^3, which describes the object's position as it moves over time.

b) To calculate the object's acceleration as a function of time, you can use the equation a(t) = -2b, since the acceleration is constant and equal to -2b. So the object's acceleration as a function of time is a(t) = -4 m/s^2.

c) To find the maximum positive displacement of the object from the origin, you can use the equation x(t) = 4t - t^3 and set the derivative equal to 0. This will give you the time at which the object reaches its maximum displacement. Plugging in this time into the original equation will give you the maximum positive displacement. In this case, the derivative is 4 - 3t^2, which equals 0 when t = √(4/3). Plugging this time into the original equation gives a maximum positive displacement of 8/3 m.
 

1. How do you calculate an object's position as a function of time?

To calculate an object's position as a function of time, you can use the formula: x(t) = x0 + v0t + 1/2at2 where x0 is the initial position, v0 is the initial velocity, a is the acceleration, and t is time.

2. What is the difference between position and acceleration?

Position refers to the location of an object in space, while acceleration refers to the rate at which an object's velocity changes over time. In other words, position tells us where an object is, and acceleration tells us how an object's position is changing.

3. Can you calculate an object's position without knowing its acceleration?

Yes, you can calculate an object's position without knowing its acceleration if you have information about its initial position and initial velocity. You can use the formula: x(t) = x0 + v0t to calculate its position at any given time.

4. How do you determine an object's acceleration from a position-time graph?

To determine an object's acceleration from a position-time graph, you can find the slope of the line connecting two points on the graph. The slope represents the object's velocity, and the change in the slope represents the object's acceleration.

5. Can an object's position and acceleration be constant at the same time?

Yes, an object's position and acceleration can both be constant at the same time. This means that the object is moving at a constant speed and in a straight line without any changes in its velocity.

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