Chapter 6.1, Problem 2E

To determine

To find out the position of the particle at $t=4$ .

Answer to Problem 2E

  $x=20$

Explanation of Solution

Given:

The velocity of the particle is given by $v(t)=2t+1$ .

Calculation:

Since v is function of t area under the curve v (t) gives the particle position. By method of midpoint rectangular approximation method (MRAM), area is divided into rectangles. Total time is divided into four equal intervals and at midpoint of interval calculates the velocity which is equal to height of rectangle then calculates the area of small rectangles then adds all the area.

  

Add all areas to get the position of particle at

  $\begin{array}{l}t=4\\ x=2+4+6+8\\ =20\end{array}$