The final velocity = initial velocity + acceleration x time

[jamiebean]

Homework Statement

attached below:

Relevant Equations

final velocity=initial velocity + acceleration x time

I first calculated initial velocity:
√7.09^2+1.07^2=7.17028

acceleration=√7.22^2+2.47^2= 7.63

then i substituted all values into this equation:
final velocity=initial velocity + acceleration x time
so, final velocity=82.0285

so the magnitude=
final velocity-initial velocity= 74.858271

is this correct?? thank you!

 

[PeroK]

Homework Statement:: attached below:
Relevant Equations:: final velocity=initial velocity + acceleration x time

View attachment 263209
I first calculated initial velocity:
√7.09^2+1.07^2=7.17028

acceleration=√7.22^2+2.47^2= 7.63

then i substituted all values into this equation:
final velocity=initial velocity + acceleration x time
so, final velocity=82.0285

so the magnitude=
final velocity-initial velocity= 74.858271

is this correct?? thank you!

It's not correct. Velocity and acceleration are vectors.

 

[PeroK]

I first calculated initial velocity:
√7.09^2+1.07^2=7.17028

Here you have calculated the initial speed.

 

[jamiebean]

Here you have calculated the initial speed.

then how can i calculate the initial velocity with the equation given? thank you!

 

[PeroK]

then how can i calculate the initial velocity with the equation given? thank you!

You are given the initial velocity. In the link you included it says so explicity.

 

[jamiebean]

You are given the initial velocity. In the link you included it says so explicity.

umm i don't understand.. instead of the form of velocity provided in the question, how can i change it into one value?

 

[PeroK]

umm i don't understand.. instead of the form of velocity provided in the question, how can i change it into one value?

Velocity is a vector quantity. In general it has three components: in the x, y and z directions (or i, j, k if you prefer).

You'll need to learn to work with vectors. You can't reduce a vector to a single value.

 

[jamiebean]

Velocity is a vector quantity. In general it has three components: in the x, y and z directions (or i, j, k if you prefer).

You'll need to learn to work with vectors. You can't reduce a vector to a single value.

then how should i calculate the magnitude of the velocity?
thank you!

 

[haruspex]

then how should i calculate the magnitude of the velocity?
thank you!

You want the magnitude of the final velocity. First, use the initial velocity vector and the acceleration vector to find the final velocity vector. Only then can you find the magnitude of that vector.

 

[jamiebean]

do i multiply the components of the initial velocity with acceleration, which i calculated as: -7.7254i,17,5123j

 

[haruspex]

do i multiply the components of the initial velocity with acceleration, which i calculated as: -7.7254i,17,5123j

Eh? Multiply a velocity by an acceleration? Certainly not.
Think: if the velocity is in ms^-1 and the acceleration is in ms^-2 that would give you something with units m²s^-3.
Besides, that is no way to multiply vectors. There are only two ways to multiply two vectors (at this level of maths): dot product and cross product. Cross product is only in 3D, so for 2D you only have the dot product. That multiplies two vectors to produce a scalar, not another vector: (a,b).(c,d)=a.c+b.d.

Use the relevant equation you quoted in post #1.

 

[hmmm27]

I don't know about the OP, but I find the notation confusing... could we not write something like:

An object has an initial velocity of $(-1.07 , 7.09)ms^{-1}$ and constantly accelerates at $(7.22 , 2.47)ms^{-2}$. What is the magnitude of the velocity after 9.81s.​

Or, is that something else. Apologies, for minor hijacking.

 

[haruspex]

I don't know about the OP, but I find the notation confusing... could we not write something like:

An object has an initial velocity of $(-1.07 , 7.09)ms^{-1}$ and constantly accelerates at $(7.22 , 2.47)ms^{-2}$. What is the magnitude of the final velocity after 9.81s.​

Or, is that something else. Apologies, for minor hijacking.

Yes, that's just another notation for the same thing. Whether it is confusing depends on what you are used to.
The $\hat i, \hat j,\hat k$ notation has benefits in writing out the expansion of a cross product.

 

[FactChecker]

Do the calculations for the $i$ and $j$ components separately, using the $i$ and $j$ components of initial velocity and acceleration. That will give you a final velocity with $i$ and $j$ components.

 

[jamiebean]

i used this equation:

final velocity=initial velocity + acceleration x time

then got the final velocity=69.7582i+31.3207j

so, the magnitude of velocity=
final velocity-initial velocity
=76.84i+24.23j

 

[haruspex]

got the final velocity=69.7582i+31.3207j

Right, but you should not quote more sig figs than in the given data. You only have 3 for acceleration, so 69.8i+31.3j

magnitude of velocity=final velocity-initial velocity

No, that would be the change in velocity. You are asked for the magnitude of the final velocity.
For a vector $\vec v=x\hat i+y\hat j$ the magnitude is $\sqrt{\vec v.\vec v}=\sqrt{(x\hat i+y\hat j).(x\hat i+y\hat j)}=\sqrt{x^2+y^2}$.

 

[jamiebean]

Right, but you should not quote more sig figs than in the given data. You only have 3 for acceleration, so 69.8i+31.3j

No, that would be the change in velocity. You are asked for the magnitude of the final velocity.
For a vector $\vec v=x\hat i+y\hat j$ the magnitude is $\sqrt{\vec v.\vec v}=\sqrt{(x\hat i+y\hat j).(x\hat i+y\hat j)}=\sqrt{x^2+y^2}$.

so, the answer should be 76.5?
thanks a lot!

 

[haruspex]

so, the answer should be 76.5?
thanks a lot!

Yes.