- #1
scrubber
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Homework Statement
The position s (in metres) of a particle, as a function of time t (in seconds), is described by the equation s=5i+4r^2j. i and j are perpendicular unit vectors.
a) Calculate the position of the particle at t=5.
b) Determine the particle's average velocity between t=0 and t=2.
c) Determine the particle's instantaneous velocity at t=4.
The Attempt at a Solution
a) When t=5,
s=5i+4(25)j=5i+100j
s=√10025=100m
b) When t=0,
s=5i=5m
When t=2,
s=5i+4(4)j=5i+16j=√281=16.76m
average velocity=displacement/time=(16.76-5)/(2-0)=5.9m/s
c) By differentiation,
v=4(2)tj=8tj
When t=4,
v=8(4)tj=32j=32m/s