How Do You Calculate Acceleration from Change in Velocity and Time?

[chocolatelover]

Homework Statement

An object moving with uniform acceleration has a velocity of 16.0 cm/s in the positive x direction when its x coordinate is 3.00 cm. If its x coordinate 1.60 s later is -5.00 cm, what is its acceleration?

Homework Equations

a=vf-vi/change in time

The Attempt at a Solution

a=3--5/1.6 s

Could someone please tell me if this looks correct?

Thank you very much

 

[XxBollWeevilx]

It looks like you are using your coordinates as the velocities...this would not be correct. Think in terms of displacement. Do you know any formulas that can be used with uniform acceleration?

 

[belliott4488]

It always helps to include the units of all the numbers in your equations. You're subtracting two numbers that have units cm and dividing them by something in seconds, so your result will be in cm/sec. That's a speed, however, not an acceleration.

As XxBollWeevilx pointed out, you need to use a different equation - one that combines just the quantities you're given and the one you're trying to solve for.

 

[chocolatelover]

Thank you very much

Does this look righ?

displacement=xf-xi

so, 3cm--5cm=displacement
=8cm

The displacement is just the distance, right?

The acceleration is:

vf-vi/change in t

I don't understand how the displacement helps. I still don't know what vi is, right?

Thank you

 

[cse63146]

distance is how much you travelled, displacement is the difference between the initial position of a reference point and any later position.

 

[XxBollWeevilx]

You're going from 3 cm to -5 cm, so your displacement will be $$x_f-x_i$$ = -5 cm - 3 cm. You DO know what vi is, from what I can see, but you don't know vf. But you don't need vf. Are there any equations that do not require vf? Think kinematics.

 

[chocolatelover]

Thank you very much

So, if the displacement=xf-xi or 3cm--5cm=8cm in this case, then I can find the velocity, right?

velocity=xf-xi/change in t

8cm/1.6-0s=5m/s

In order to find the acceleration, I need to take vf-vi/change in t and it needs to be in m/s^2, right?

I know that the acceleration in uniform or constant. I know that vf=vi+at, but I don't know what vi or a are. Could you show me what I need to do to find the acceleration?

Thank you

 

[cse63146]

its -5 cm - 3 cm not 3cm--5cm

displacement can be negative, distance cant

 

[XxBollWeevilx]

No, don't worry about finding velocity. Taking xf-xi/change in t will only give you the average velocity during the motion, not the initial or final velocity. Look for a formula that doesn't require vf and everything but a is known.

 

[chocolatelover]

Thank you very much

Could I use this equation?

xf=xi+vit+1/2at^2?

Thank you

 

[XxBollWeevilx]

That would be a very good equation to use! :)

Nice job.

 

[chocolatelover]

Thank you very much

Does this look correct?

-5=16+16(1.6)+1/2a1.6^2
a=-36.41

Thank you

 

[XxBollWeevilx]

I didn't check the arithmetic, but that looks pretty good to me.

 

[chocolatelover]

Thank you very much

Regards

 

[chocolatelover]

Could someone please check this? I want to make sure I'm doing it right.

Thank you

 

[chocokat]

Thank you very much

Does this look correct?

-5=16+16(1.6)+1/2a1.6^2
a=-36.41

Thank you

The first 16 should be x1, i.e. 3. Be careful of these little errors!

 

[chocolatelover]

Thank you very much

The first 16 should be x1, i.e. 3. Be careful of these little errors!

What do you mean x1, i.e. 3? It should be multiplied by 1?

Thank you

 

[chocokat]

This is the equation you are using:

Thank you very much

Could I use this equation?

xf=xi+vit+1/2at^2?

Thank you

What is the value of xi, and what is the value you used when you calculated it?
(I'm sorry, I used x1 above when I should have used xi)

 

[chocolatelover]

It's okay. It should have been 3, right? Does -26.25 look alright?

 

[chocokat]

It's okay. It should have been 3, right?

Yeah, you've got it now.

 

[chocolatelover]

Thank you very much

Regards