How Do You Calculate the Magnitude of Acceleration for a Particle in Motion?

AI Thread Summary
To calculate the magnitude of acceleration for a particle in motion defined by its x, y, and z coordinates as functions of time, one must first find the second derivatives of each coordinate with respect to time. The acceleration is a vector, and its magnitude is determined by combining these components using the formula |a| = √(x''² + y''² + z''²). The discussion emphasizes that simply adding the second derivatives is incorrect; the correct approach involves calculating the square root of the sum of the squares of the components. The specific example provided involves evaluating the acceleration at t = 3.00 seconds. Understanding vector properties is crucial for accurate calculations in physics.
schrock
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A location of a particle is given in m by x, y and z coordinates as function of time in s as:
x= -11+9t+11t^2
y= -23-21t
z= -93+25t+11t^2

What is the magnitude of the objects acceleration at t= 3.00s?

Would I add the second derivatives for magnitude?
 
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Hi schrock! :smile:
schrock said:
A location of a particle is given in m by x, y and z coordinates as function of time in s as:
x= -11+9t+11t^2
y= -23-21t
z= -93+25t+11t^2

What is the magnitude of the objects acceleration at t= 3.00s?

Would I add the second derivatives for magnitude?

You mean |a| = x'' + y'' + z'' ?

Nooo …

Acceleration is a vector (just like velocity :wink:).

So its magnitude is calculated from its components the same way as for any vector. :smile:
 

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