Question

An object moves with velocity as given in the graph below (in ft/sec) How far did the object travel from t = 0 tot t = 40 ?

Answer 1

We are given the graph of the velocity as a function of time.

It's required to find the distance traveled by the object from t = 0 to t = 40 seconds.

Since the graph is a line, the distance can be found by computing the area under the line as shown in the figure below:

The shape of the region is a trapezoid with vertical parallel sides (bases).The shape of the region is a trapezoid

The length of the bases are b1 = 4 ft/s and b2 = 7 ft/s. The height of the trapezoid is h = 40 sec.

Now apply the formula of the area of a trapezoid:

$A=\frac{b_1+b_2}{2}\cdot h$

Plugging in the given values:

$A=\frac{4\text{ ft/s}+7\text{ ft/s}}{2}\cdot40\text{ sec}$

Calculating:

A = 220 ft

The object travels 220 ft