An object moves along a line with velocity v(t)= cases 2t-4, & 0 t<3, - ,t+5, & 3 t 7

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

Problem

An object moves along a line with velocity

v(t)=\begin{cases} 2t-4, & 0\le t<3,\\ -\,t+5, & 3\le t\le 7. \end{cases}

Time

t

is measured in seconds and

v

in meters per second. (1) Determine all

t

[0,7]

for which the object’s speed is increasing. (2) Determine all

t

[0,7]

for which the object’s speed is decreasing.