Find the velocity and position vectors of a particle that has the given accelera

Question

Find the velocity and position vectors of a particle that has the given acceleration and the given initial velocity and position. a(t) = 5i + 8j, v(0) = k, r(0) = i v(t) = r(t) = Find the position vector of a particle that has the given acceleration and the specified initial velocity and position, a(t) = 16ti + sintj + cos2tk, v(0) = i, r(0) = j r(t) = On your own using a computer, graph the path of the particle. Find the position vector of a particle that has the given acceleration and the specified initial velocity and position. a(t) = 11ti + etj + e-tk, v(0) = k, r(0) = j + k r(t) = On your own using a computer, graph the path of the particle.

Explanation / Answer

a(t) = 5i + 8j

v(t0 = integration of a(t)

v(t) = 5ti + 8tj + c

v(0) = 1k

So, c=0

So, v(t) = 5ti + 8tj + k

to find s(t),

r(t) = 5t^2/2 i + 4t^2j + tk + c1

r(0)= i

So, at t=0, c1 = i

so, r(t) = (5t^2/2 +1)i + 4t^2j + tk

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