The position of a particle in space at time t is r(t) as shown below. Find the p
ID: 1771821 • Letter: T
Question
The position of a particle in space at time t is r(t) as shown below. Find the particle's velocity and acceleration vectors. Then find the particle's speed and direction of motion at
t=1. Write the particle's velocity at that time as the product of its speed and direction.
(a) The particle's velocity is ___ i + ___ j + ___ k
(b) The particle's acceleration is ___ i + ___ j + ___ k
(c) The particle's speed at t = 1 is ___
(d) The particle's direction at t = 1 is ___ i + ___ j + ___ k
r(t) = (4 ln (1+1))i + tl + 4kExplanation / Answer
a)
r(t) = (4 ln(t + 1)) i + t2 j + (0.25) t2 k
velocity is given as
v(t) = dr(t)/dt = (4/(t + 1)) i + 2t j + (0.5) t k
at t = 1
v(1) = 2 i + 2 j + (0.5) k
b)
acceleration is given as
a(t) = dv(t)/dt = (- 4/(t + 1)2) i + 2 j + (0.5) k
at t = 1
a(1) = - 1 i + 2 j + (0.5) k
c)
speed = sqrt(22 + 22 + 0.52) = 2.87 m/s
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