Respuesta :
Therefore, the velocity of the particle at time t is given as:
[tex]v = 2t^3-4.5t^2-4t+6[/tex]
The velocity of the particle at the first instance the particle at the origin is 6m/s
The given expression is:
[tex]x(t)=0.5t^4 - 1.5t^3 - 2t^2 + 6t - 1[/tex]
This expression [tex]x(t)=0.5t^4 - 1.5t^3 - 2t^2 + 6t - 1[/tex] represents the position of the particle
The velocity of the particle will be gotten by finding the derivative of x(t) as shown below
[tex]\frac{dx}{dt} = 0.5(4)t^3-1.5(3)t^2-2(2)t+6\\\\ \frac{dx}{dt} = 2t^3-4.5t^2-4t+6[/tex]
Therefore, the velocity of the particle at time t is given as:
[tex]v = 2t^3-4.5t^2-4t+6[/tex]
The velocity of the particle at the first instance the particle at the origin
That is, t = 0
Substitute t = 0 into the equation for the velocity, v
[tex]v = 2t^3-4.5t^2-4t+6[/tex]
[tex]v=2(0)^3-4.5(0)^2-4(0)+6\\\\v=6 m/s[/tex]
The velocity of the particle at the origin is 6 m/s
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