Step-by-step explanation:
1. Given: a = 4t + 4
We know that
By definition, the integral of a power function x^n is
Integrating the acceleration <em>a</em>, we get
where k = constant of integration. We know that v = 10 when t = 0 so when we do the substitution, we get k = 10 therefore, the final expression for v is
To find s, we need to integrate v. Knowing that
where k once again is the constant of integration. We know that s = 2 when t = 0, which gives us k = 2. Therefore, the final expression for <em>s</em> is
2. The potential difference <em>V</em> between two boundaries <em>a</em> and <em>b</em> is given by
Note that the integral in the expression above can be rewritten and the integrated as
so the potential difference <em>V</em> is then J