How Do You Calculate Velocity and Acceleration from a Position Vector?

[Seven of Nine]

Homework Statement

The position vector of an object of mass 0.10 kg at time t in seconds is given by
=(^3+5)−4+2^2
Find the velocity and the acceleration as a function of t

Homework Equations

=(^3+5)−4+2^2

The Attempt at a Solution

For velocity I think the equation needs to be differentiated giving; 3t^2i+5i-4j+4tk

To find the magnitude I have to find the square root of the squares of the value of each vector quantity - but no idea what to do about the square or how to find the acceleration.

Dont need the answers just the information needed to find the values and where I'm going wrong and what I can't remember

 

[mfb]

=(^3+5)−4+2^2

It looks like something went wrong with the notation here.

For velocity I think the equation needs to be differentiated

Right.

To find the magnitude I have to find the square root of the squares of the value of each vector quantity

Of the sum of squares, yes.

but no idea what to do about the square

What is unclear?

or how to find the acceleration.

What is the relation between velocity and acceleration?

 

[Seven of Nine]

It looks like something went wrong with the notation here.Right.Of the sum of squares, yes.What is unclear?What is the relation between velocity and acceleration?

Yes sorry the equation is
r=(t^3+5t)i−4tj+2t^2k

and do I have to do anything with the t^2 value and what do I do about the 3t^2i +5i how do I find the sum of the square of of i? And yes after I asked about the acceleration I realized I was being a bit thick. Thank you

 

[haruspex]

how do I find the sum of the square of of i

The magnitude of a vector is given by ##|\vec v|=\sqrt{\vec v.\vec v}##, where the dot represents the dot product. Do you know how to find the dot product of ##x\hat i+y\hat k## with itself?