Question

A particle moves in a straight line with the given velocity v(t) = 2t−2 − 2 (in meters per second). Find the displacement and distance traveled over the time interval [0.5, 2].

Answer 1

The answer is -2.25 units.

Step-by-step explanation:

Total displacement of particle moves in a straight line with the given velocity v(t) = 2t−2 − 2 will be:

`x=\int\limits^2_(0.5) {2t-2-2} \, dt\\x=\int\limits^2_(0.5) {2t} \, dt+ \int\limits^2_(0.5) {-4}\, dt \\x=3.75-6\\x=-2.25`