# Velocity and acceleration vectors and their magnitudes

• MHB
• WMDhamnekar
In summary, the conversation discusses how to calculate the magnitudes of velocity and acceleration vectors at t=0 for a given set of equations. The formula for finding the magnitude of a vector is also mentioned.
WMDhamnekar
MHB

How to answer this question? I am working on this question. Any math help, hint or even correct answer will be accepted.

Differentiate them to get velocities and accelerations in x, y, z(i, j, k ) directions. Add them vectorially to get resultant velocity and acceleration.

$v=\sqrt{37}, a= \sqrt{325}$ at t=0

so? what problem are you facing? Once you get velocity and acceleration, calculate the magnitude by $\sqrt[]{a^2 + b^2 +c^2}$ where a vector is given by $a i + b j + c k$

DaalChawal said:
so? what problem are you facing? Once you get velocity and acceleration, calculate the magnitude by $\sqrt[]{a^2 + b^2 +c^2}$ where a vector is given by $a i + b j + c k$
Answers given are magnitudes of velocity and acceleration vectors at t=0. What are you talking about?

$x= e^{-t}$

$v_x = - e^{-t}$

$a_x = e^{-t}$
similarly calculate velocity and acceleration in $y, z$ directions.
Then
You will get velocity as $- e^{-t} i +(-6)sin(3t) j + 6cos(3t) k$
Now put t=0 to get velocity at t=0nand calculate the magnitude.
for acceleration try yourself

DaalChawal said:
$x= e^{-t}$

$v_x = - e^{-t}$

$a_x = e^t$
similarly calculate velocity and acceleration in $y, z$ directions.
Then
You will get velocity as $- e^{-t} i +(-6)sin(3t) j + 6cos(3t) k$
Now put t=0 to get velocity at t=0nand calculate the magnitude.
for acceleration try yourself
I already computed velocity and acceleration vectors. But i only posted here their magnitudes.

Okay then use formula that if a vector is expressed as $x = a i + b j + c k$ then its magnitude is given by $|x| = \sqrt[]{a^2+b^2+c^2}$

Since this has been sitting a while, yes, the answers given in post #3 are corret.

We have x= e^{-t}, y= 2 cos(3t), and z= 2 sin(3t).
The velocity is given by x'= -e^{-t}, y'= -6 sin(3t), and z'= 6 cos(3t).
The acceleration is given by x''= e^{-t}, y''= -18 cos(3t), and z''= -18 sin(3t).

|v(0)|= sqrt{1+ 0+ 36}= sqrt{37}
|a(0)|= sqrt{1+ 324+ 0}= sqrt{325}

## 1. What is the difference between velocity and acceleration?

Velocity is a vector quantity that describes the rate of change of an object's position over time. It includes both the magnitude (speed) and direction of the object's motion. Acceleration, on the other hand, is also a vector quantity that describes the rate of change of an object's velocity over time. It includes both the magnitude and direction of the change in velocity.

## 2. How are velocity and acceleration vectors represented?

Velocity and acceleration vectors are typically represented graphically as arrows. The length of the arrow represents the magnitude of the vector, while the direction of the arrow represents the direction of the vector. The arrows are drawn on a coordinate system, with the x-axis representing time and the y-axis representing the magnitude of the vector.

## 3. What is the magnitude of a velocity or acceleration vector?

The magnitude of a velocity or acceleration vector is its length or size. It is represented by a number and a unit of measurement, such as meters per second (m/s) for velocity and meters per second squared (m/s^2) for acceleration. The larger the magnitude, the faster the object is moving or the greater the change in velocity.

## 4. How do you calculate the magnitude of a velocity or acceleration vector?

To calculate the magnitude of a velocity or acceleration vector, you can use the Pythagorean theorem. This involves squaring the x and y components of the vector, adding them together, and then taking the square root of the sum. The resulting number is the magnitude of the vector. For example, if the x component is 3 and the y component is 4, the magnitude would be √(3^2 + 4^2) = 5.

## 5. Can the magnitude of a velocity or acceleration vector be negative?

Yes, the magnitude of a velocity or acceleration vector can be negative. This indicates that the vector is pointing in the opposite direction of its positive counterpart. For example, a velocity vector with a magnitude of -5 m/s would be moving in the negative direction on the x-axis. However, the magnitude itself is always represented as a positive number.

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