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Position of a particle moving along x-axis is given by x = 3t - 4t2 + t3, where x is in meters and t in seconds.
(a)Find the position of the particle at t = 2 s.
(b)Find the displacement of the particle in the time interval from t = 0 to t = 4 s.
(c)Find the average velocity of the particle in the time interval from t = 2s to t=4s.
(d)Find the velocity of the particle at t = 2 s.
(a) x(t) = 3t - 4t2 + t3
=> x(2) = 3 x 2 - 4 x (2)2 + (2)3 = 6 - 4 x 4 + 8 = -2m.
(b) x(o) = 0
X(4) = 3 x 4 - 4 x (4)2 + (4)3 = 12 m.
Displacement = x(4) - x(0) = 12 m.
(c) = X(4)X(2)/(4-2) = (12-(-2))/2 m/s = 7 m/s
(d) dx/dt = 3 - 8t + 3t2
v(2) (dx/dt)2 = 3 - 8 x 2 + 3 x (2)2 = -1m/s
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