The displacement of a particle moving along the -axis is s(t)=e^ -2t , (kt) metres
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
The displacement of a particle moving along the x-axis is
s(t)=e−2tsin(kt) metres,
where k>0 is a constant and t is in seconds.
(i) If the initial velocity of the particle is 3ms−1, determine the value of k.
(ii) For the value of k found in part (i), find the velocity v(t) and acceleration a(t) of the particle.
(iii) Find the smallest positive time at which the particle comes to instantaneous rest.
(iv) Determine the acceleration of the particle at the time obtained in part (iii).