1.A particle is moving in 3D space, describedas x = 3t3, y = 2t+5, z = t2Find the velocity vector of the particle as a function of time, usingi, j, k notation Find the magnitude of the velocity as a function of time Find the magnitude of the velocity when t = 4 sec Find the acceleration vector as a function of time, usingi, j, k notation Find the magnitude of acceleration when t = 4 sec

Question
Asked Sep 10, 2019
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1.
A particle is moving in 3D space, describedas x = 3t3, y = 2t+5, z = t2
Find the velocity vector of the particle as a function of time, using
i, j, k notation
 
Find the magnitude of the velocity as a function of time
 
Find the magnitude of the velocity when t = 4 sec
 
Find the acceleration vector as a function of time, using
i, j, k notation
 
Find the magnitude of acceleration when t = 4 sec
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Expert Answer

Step 1

Write the expression for the displacement of the particle in all the directions as given in the question.

s(1)3r
(t) 21 +5
s.()
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s(1)3r (t) 21 +5 s.()

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Step 2

Write the expression for the displacement in vector form as mentioned below.

s(t)sisjsk
-(3)i+ (21+5) (f)k
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s(t)sisjsk -(3)i+ (21+5) (f)k

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Step 3

Differentiate the above function wit...

ds
vt)=
dt
d
(r+(2+5)()k)
dt
(9r?)i (2)i+(21)k
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ds vt)= dt d (r+(2+5)()k) dt (9r?)i (2)i+(21)k

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