The equation of motion of a particle is given by,
s = [tex] 2t^{3} - 8t^{2} + 4t +2 [/tex]
Let velocity of particle is denoted by v.
The velocity of the particle is given by,
velocity (v) = [tex] \frac{ds}{dt} [/tex]
v = [tex] \frac{d}{dt} [ 2t^{3} - 8t^{2} + 4t +2 ] [/tex]
v = [tex] \frac{d}{dt} 2t^{3} - \frac{d}{dt} 8t^{2} + \frac{d}{dt} 4t + \frac{d}{dt} 2 [/tex]
v = [tex] 6t^{2} -16t +4 [/tex]
Thus, Velocity of particle is given by,
v = [tex] 6t^{2} -16t +4 [/tex]
Let acceleration of the particle is denoted by a.
The acceleration of particle is given by,
Acceleration = [tex] \frac{dv}{dt} [/tex]
a = [tex] \frac{d}{dt} [6t^{2} -16t +4] [/tex]
a = [tex] \frac{d}{dt} 6t^{2} -\frac{d}{dt}16t +\frac{d}{dt}4 [/tex]
a = 12t - 16
Thus, acceleration of the particle is given by,
a = 12t - 16
