Parametric equations -> acceleration

T, time of transit from r1 to r2. 4. a = (ax^2 + ay^2)^1/2In summary, the magnitude of the object's acceleration is equal to the square root of the sum of the squared accelerations along each axis, calculated separately using the given equations for the object's position and velocity at two different times.
  • #1
burton95
54
0
parametric equations --> acceleration

Homework Statement



An object is moving at constant acceleration in the x-y plane. Its position and velocity at two different times are given by the following equations:
What is the magnitude of the object’s acceleration (in m/s2) as it moves from the first position to the second position? Hint: solve for the acceleration along each axis separately.

Homework Equations


r1= (2m)i + (4m)j
r2= (10m)i + (14m)j

v1= (1m/s)i + (8m/s)j
v2= (7m/s)i + (2m/s)j

The Attempt at a Solution



I decided to calc magnitude of the velocity

[itex]\left\|[/itex]v1[itex]\right\|[/itex] = (82+12)1/2 = 8.06

mag v2 = (72 + 22)1/2 = 7.2801

(Vf)2=(Vi)2 + 2asΔs

for y
(7.2801)2=(8.06)2+2as(10)
as = -.7457725

for x
(7.2801)2=(8.06)2+2as(8)
as = -.59818

√((-.598182)+(-.74577252) = .95755
 
Last edited:
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  • #2


I would follow your instructor's hint and work with one coordinate at a time. Your eq's. don't make sense to me.

BTW I think you have to assume constant acceleration in this problem.

You might try the following:

1. write eq. for vx(t).
2. write eq. for x(t).

Eq's. 1 and 2 give you ax and T, the time of transit from r1 to r2.
3. do same for y.
 

What are parametric equations?

Parametric equations are a set of mathematical equations that describe the relationship between two or more variables. In the context of acceleration, parametric equations can be used to represent the position, velocity, and acceleration of an object over time.

How are parametric equations used to calculate acceleration?

Parametric equations can be used to calculate acceleration by using the derivatives of the position and velocity equations. The second derivative of the position equation represents the acceleration of the object at a given time.

What are the advantages of using parametric equations to study acceleration?

One advantage of using parametric equations to study acceleration is that they can represent complex motion patterns, such as circular or projectile motion. They also allow for a more precise analysis of acceleration over time.

How do parametric equations differ from Cartesian equations?

Parametric equations differ from Cartesian equations in that they use parameters, or variables, to represent the relationship between two or more variables. Cartesian equations, on the other hand, use x and y coordinates to represent a relationship between two variables.

Can parametric equations be used in real-world scenarios?

Yes, parametric equations can be used to model and analyze real-world scenarios involving acceleration, such as the motion of a projectile or a rollercoaster. They can also be used to design and optimize systems that involve acceleration, such as a rocket launch or a car engine.

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