# The final velocity = initial velocity + acceleration x time

• jamiebean
In summary: But you should keep more digits internally. For example, if you use the value calculated in post #16, you will get 76.8415, and rounding to 3 digits gives 76.8. But if you use 31.3207 for the ##j## component you get 76.5337, rounding to three digits gives 76.5. So the answer depends on how many digits you keep. It is better to keep more digits internally and only round the final answer.Yes. But you should keep more digits internally. For example, if you use the value calculated in post #16, you will get 76.8415, and rounding to 3 digits gives
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!

jamiebean said:
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.

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

Here you have calculated the initial speed.

PeroK said:
Here you have calculated the initial speed.
then how can i calculate the initial velocity with the equation given? thank you!

jamiebean said:
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.

PeroK said:
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?

jamiebean said:
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.

PeroK said:
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!

jamiebean said:
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.

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

jamiebean said:
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.

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.

Last edited:
hmmm27 said:
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.

hmmm27
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.

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

jamiebean said:
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
jamiebean said:
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}##.

haruspex said:
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!

jamiebean said:
so, the answer should be 76.5?
thanks a lot!
Yes.

## 1. What is the formula for calculating final velocity?

The formula for calculating final velocity is: final velocity = initial velocity + acceleration x time.

## 2. How is initial velocity defined in this formula?

Initial velocity refers to the starting velocity of an object or body in motion.

## 3. What does acceleration represent in this formula?

Acceleration represents the rate of change of an object's velocity over time. It can be positive (speeding up) or negative (slowing down).

## 4. Is time measured in seconds in this formula?

Yes, time is typically measured in seconds when using this formula. It is important to ensure that the units for time and acceleration are consistent.

## 5. Can this formula be used for any type of motion or only linear motion?

This formula can be used for linear motion, where an object moves in a straight line. It may also be used for certain types of rotational motion, such as constant angular acceleration.

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