A particle moves in the plane so that

MATHEMATICS · Multi-part · A Level · Mathematics · Differentiation · Differentiation

Problem

A particle moves in the plane so that, for each real number

t

, its position is given by the parametric equations

x(t)=t^{2}+1,\\ y(t)=3t-2.

Answer the following questions about the motion of the particle. (1) Determine the coordinates of the particle when

t=2

. (2) Find

\dfrac{dy}{dx}

t=2

. (3) Using your results, write the equation of the tangent line to the particle’s path at

t=2

in point–slope form. (4) Rewrite the equation from part (c) in slope–intercept form.