Can someone please solve the following question for me showing all work. For the parametric function of motion of an object, find the velocity and acceleration of theobject at the given time.8.x = 16√t16y=.t=2Velocity:Acceleration:

Solution: Given x = 16t , y= 16t and t=2 The velocity of an object whose motion is described by…

Answered: For the parametric function of motion…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Can someone please solve the following question for me showing all work.

For the parametric function of motion of an object, find the velocity and acceleration of the
object at the given time.
8.
x = 16√t
16
y=.
t=2
Velocity:
Acceleration:

Expert Solution

Step 1

Solution:

Given x = $16 \sqrt{t}$ , y= $\frac{16}{t}$ and t=2

The velocity of an object whose motion is described by a parametric equation is,

$v (t) = \sqrt{(x' {(t))}^{2} + (y' {(t))}^{2}} \to (1) W h e r e x' (t) a n d y' (t) a r e t i m e d e r i v a t i v e s o f x a n d y c o o r d i n a t e s$

The acceleration of an object whose motion is described by a parametric equation is,

$a (t) = \sqrt{(x " {(t))}^{2} + (y " {(t))}^{2}} \to (2) W h e r e x " (t) a n d y " (t) a r e s e c o n d t i m e d e r i v a t i v e s o f x a n d y c o o r d i n a t e s$