Question

Write the general expression of v vector and a vector (velocity and acceleration) in 3 dimension

Answer 1

Answer:

Calculate the acceleration vector given the velocity function in unit vector notation.

Describe the motion of a particle with a constant acceleration in three dimensions.

Use the one-dimensional motion equations along perpendicular axes to solve a problem in two or three dimensions with a constant acceleration.

Express the acceleration in unit vector notation.

Answer 2

The general expression of velocity and acceleration in 3 dimension respectively is

$v_x\hat i+v_y\hat j+v_z\hat k$ and $a_x\hat i+a_y\hat j+a_z\hat k$

Explanation:

In three dimension, the general expression of a velocity vector can be written as

$\vec v=v_x\hat i+v_y\hat j+v_z\hat k$

Where,

$\v_x$ is the component of velocity along the x-axis

$\v_y$ is the component of velocity along the y-axis

$\v_z$ is the component of velocity along the z-axis

Also

The general expression of acceleration vector can be written as

$\vec a=a_x\hat i+a_y\hat j+a_z\hat k$

Where,

$a_x$ is the component of acceleration along the x-axis

$a_y$ is the component of acceleration along the y-axis

$a_z$ is the component of acceleration along the z-axis

Hope this answer is helpful.

Know More:

Q: What is the general formula for acceleration? ​

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