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A particle moves in a straight line such that its velocity, vms−1, after t seconds is given by v(t)=2t3−kt2+4t.
Determine the initial velocity of the particle.
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Give an expression for the acceleration a(t).
It is given that the displacement of the particle after t=4 seconds is 32m.
Show that k=6.
Calculate the distance travelled by the particle in this time.
Find an expression for the displacement s(t) of the particle from the origin.
Hence or otherwise, find the time at which the displacement is at a maximum between t=0 and t=2 seconds, and find this maximum displacement.
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