Question

A particle moves along a trajectory given by p(t) = <6t, (2 + 3t - 2t^2)>. What is the particle's displacement during the time period t [1,3]?

Do we just sub in t as appropriate (e.g. 6(1), (2+3(3) - 2(3)^2)? Or am I missing something here.

Answer 1

Displacement is a vector obtained by the difference between final and initial positions, so

displacement during t[1,3]
=p(3)-p(1)

You can leave the result in vector form <δx, δy>.

Note: subtraction is done component by component, ex.
<7,4>-<2,3>=<5,2>