A particle moving in the xy plane undergoes a displacement given by ?vector r =

Question

A particle moving in the xy plane undergoes a displacement given by ?vector r = (2.4 i + 2.9j) m as a constant force vector F = (4.0i + 1.9j) N acts on the particle.

A particle moving in the xy plane follows a path described as a function of time by vector r (t) = (3.8 m/s)ti - (1.9 m/s2)t2j. A constant force given by vector F = (5.0i - 2.0j) N acts on the particle (note that other forces must act on the particle as well if it follows the path given above).

(a) Determine the displacement of the particle during the interval ti = 1.0 s to tf = 4.0 s.
?vector r = i m - j m

(b) Calculate the work done by vector F during this interval.
W = J

Explanation / Answer

a) At t = 1 s, position r(1) = 3.8*1 i - 1.9*1^2 j = 3.8i - 1.9j

At t = 4 s, position r(4) = 3.8*4 i - 1.9*4^2 j = 15.2i - 30.4j

Displacement = r(4)-r(1) = (15.2i - 30.4j) - (3.8i - 1.9j) = 11.4i - 28.5j

b) Work done = F.r = (5i - 2j).(11.4i - 28.5j) = 5*11.4 + (-2)(-28.5) = 114 J

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