Question

The position of a particle moving along an x axis is given by x = 12t2 - 2t3, where x is in meters and t is in seconds. Determine

(a) the position,

(b) the velocity, and

(c) the acceleration of the particle at t = 3.0 s. Determine the average velocity of the particle between t = 0 and t = 3s.

Answer 1

a) x = 12t^2 - 2t^3

x at t = 3  

= 12*3^2 - 2*3^3

= 54 m

(b) v = dx/dt = 24t - 6t^2

v at t= 3 , 24*3 - 6*3^2

= 18 m/s

(c) a = dv/dt = 24 - 12t

a at t = 3 , 24 - 12*3 = -12 m/s2

average velocity at t = 0 and t= 3

= x(3) - x(0) / 3 = 54 - 0 / 3 = 18 m/s