We are given that an object starts with an initial velocity of 5 m/s and that we are required to determine its velocity after 2 seconds. We are given the area of acceleration vs time. In a graph of acceleration vs time, the area under the curve represents the velocity of the object under the given acceleration.
We can determine the velocity reached by the object between t = 0 and t = 2 finding the area under the curve. Since the acceleration is constant the area under the curve is a square, therefore:
[tex]v=(2\frac{m}{s^2})(2s)=4\frac{m}{s}[/tex]This is the velocity after the object starts accelerating the final velocity is determined by adding the initial velocity therefore, the final velocity is:
[tex]v_f=4\frac{m}{s}+5\frac{m}{s}=9\frac{m}{s}[/tex]