Question

The position of a particle s given by: r = 4t2ī + sin (2t), with position and time in meters and seconds respectively. Find its velocity. (5) Since the problem does not specify any requirements, you are free to express the vector using any format you choose. Pick something convenient.

Answer 1

5.

Position of particle is given by:

r = 4t² i + sin (2t) j

Velocity of particle is given by:

V = dr/dt

Now remember that

d(xⁿ)/dx = nx^n-1

d(sin (nx))/dx = n*cos (nx)

So Using these

V = d[4t² i + sin (2t) j]/dt

V = 4*2*t^2-1 i + 2*cos (2t) j

V = 8t i + 2*cos (2t) j

In Vector form

$\vec{V} = 8t \; \; \hat{i} + 2cos (2t)\: \: \hat{j}$

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