For a particle moving along a straight line

MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

For a particle moving along a straight line, its displacement

x

(in metres) from the origin varies with time

t

(in seconds) as follows:

x = t^{2}\quad \left(0 \le t \le 2\right)

x = 4t + C\quad \left(2 < t \le 5\right)

Answer the following: (a) Part 1: (i) Determine the constant

C

so that the displacement is continuous at

t = 2\,\text{s}

. (b) Part 2: (ii) Sketch the velocity–time graph for the interval

0

5\,\text{s}

, clearly indicating the values at

t = 0

2\,\text{s}

, and

5\,\text{s}