Finding Velocity and Acceleration based on position of X & Y

[Lori]

1. Homework Statement
Given x and y position ... find magnitude of both velocity and acceleration and their direction at t = 2 ?

x = 4t
y = 30 - 2.2t^2

would the velocity's magnitude be sqrt(8^2 + 8.8^2) ?

Homework Equations

v = sqrt(vy^2 + vx^2)

The Attempt at a Solution

vy = -8.8
vx= 8

v = sqrt((8)^2 +(-8.8^2)) = 11.89 m/s

atan(8/) = 42 degrees east of south

Is this how I'm suppose to find velocity?

 

[Ray Vickson]

Homework Statement

Given x and y position ... find magnitude of both velocity and acceleration and their direction at t = 2 ?

x = 8t
y = 30 - 2.2t

would the velocity's magnitude be sqrt(8^2 + 2.2^2) ?

Homework Equations

v = sqrt(vy^2 + vx^2)

The Attempt at a Solution

vy = -2.2
vx= 8

v = sqrt((-2.2)^ +(8^2)) = 9.1 m/s

atan(-2.2/8) = 15 degrees east of south

Is this how I'm suppose to find velocity?

That is how I would have done it, but I would have described arctan(-2.2/8) correctly. A a simple sketch would reveal what is wrong with your description of the angle.

 

[Lori]

That is how I would have done it, but I would have described arctan(-2.2/8) correctly. A a simple sketch would reveal what is wrong with your description of the angle.

Would it be 15 degrees south of east?

 

[Lori]

Would it be 15 degrees south of east?

And is acceleration just derivative of velocity so
v = (8)i + 4.4t(j)
a = 0 - 4.4 = -4.4 m/s^2 ? How do i find direction of velocity? Would it be directly southward?

 

[I like Serena]

Would it be 15 degrees south of east?

Yep.

And is acceleration just derivative of velocity so
v = (8)i + 4.4t(j)
a = 0 - 4.4 = -4.4 m/s^2 ? How do i find direction of velocity? Would it be directly southward?

How did you get that v?
Edit: Oh, I see you updated the problem statement.
Can we find vx and vy as derivatives of x and y -- without substituting t?
And then find ax and ay as derivatives of vx and vy?

 

[Ray Vickson]

Would it be 15 degrees south of east?

Yes.

 

[Ray Vickson]

And is acceleration just derivative of velocity so
v = (8)i + 4.4t(j)
a = 0 - 4.4 = -4.4 m/s^2 ? How do i find direction of velocity? Would it be directly southward?

The acceleration is a vector, not a scalar, so you need to include the i and j unit vectors in your expression for a. Then you will be able to answer your own question---a habit you should develop as part of your learning process.

 

[Lori]

How do i know if i should give my answer in vector form cause the problem i have is that it asked to give the magnitude . Isnt magnitude just the numerical value?

I have to solve many physics problems involving the x and y directions for velocity, acceleration, position... but like i get confused on whether i should include vector units or not.

This is basically the reason why I wanted to make sure that i was answering the question right. I was confused on whether i should use the pythagorean formula and square the x and y components to get the velocity/acceleration OR if i was suppose to use the Kinematic equations and plug in numbers and solve

 

[Ray Vickson]

How do i know if i should give my answer in vector form cause the problem i have is that it asked to give the magnitude . Isnt magnitude just the numerical value?

I have to solve many physics problems involving the x and y directions for velocity, acceleration, position... but like i get confused on whether i should include vector units or not.

This is basically the reason why I wanted to make sure that i was answering the question right. I was confused on whether i should use the pythagorean formula and square the x and y components to get the velocity/acceleration OR if i was suppose to use the Kinematic equations and plug in numbers and solve

The question asked you to find the magnitude and direction for both velocity and acceleration. Anyway, I was really objecting to your writing velocity v as a vector on one line and acceleration a as a scalar on the very next line. You would be better off writing vectors using a bold font, such as v; then the magnitude of that vector could be written as v (not bold) or |v| or |v|.

 

[I like Serena]

In this case we have to find the vector components first, before we can find the magnitude and direction.