Answer:
The velocity is 8 m/s and acceleration is 8 [tex]m/s^{2}[/tex]
Explanation:
The motion of the particle is given by:
[tex]v^{3}[/tex]=[tex]x^{3\\}[/tex]
or, v= x .................................1
substitute x= 8m,
v= 8 m/s
Now differentiate it with respect to time (t),
[tex]\frac{dv}{dt}[/tex] = [tex]\frac{dx}{dt}[/tex]
or, [tex]\frac{dv}{dt}[/tex] = v
∴ [tex]\frac{dv}{dt}[/tex] = v
now substitute the value of v from equation 1,
[tex]\frac{dv}{dt}[/tex] = x
now at, x= 8
[tex]\frac{dv}{dt}[/tex] = 8
∴ [tex]\frac{dv}{dt}[/tex] = 8 [tex]m/s^{2}[/tex]
As
[tex]\frac{dv}{dt}[/tex] = acceleration
So the acceleration of the particle at x=8m is 8 [tex]m/s^{2}[/tex] .
