the expressions for the three rectangular components of acceleration is x²z²+y²z
Typically, a's direction does not coincide with the particle's route. The second derivative of the velocity vector (second derivative of the position vector) is the acceleration vector. dv/dt = d2r/dt2 = a.
From expression for velocity , u=x
v=x²z
w=yz
aₓ=[tex]\frac{∂u}{∂t} + u \frac{∂u}{∂t}+ v \frac{∂u}{∂t}+w\frac{∂u}{∂t}[/tex]
Then aₓ = 0+ ( x) (1) + x²z(0)+yz(0)
=x
similarly ay=[tex]\frac{∂u}{∂t} + u \frac{∂u}{∂t}+ v \frac{∂u}{∂t}+w\frac{∂u}{∂t}[/tex]
then ay= 0 + (x)(2xz)+(x²z)(0)+(yz)(x²)
= 2x²z+x²yz
also,
az=[tex]\frac{∂u}{∂t} + u \frac{∂u}{∂t}+ v \frac{∂u}{∂t}+w\frac{∂u}{∂t}[/tex]
so that az=
0+(x)(0)+x²z(z)+yz(y)
=x²z²+y²z
the expressions for the three rectangular components of acceleration is x²z²+y²z
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