Kinematics Differential Equations Assignment

In class we solved the following differential equations governing the velocity and position of an object falling through the atmosphere near the surface of the earth,

Dv/ dt =9.8- v/5 dx/dt =49(1-e^-t/5)

subject to the initial conditions v(0) = 0 and x(0) = 0. In solving these equations, we evaluated indefinite integrals which gave an arbitrary integration constant in each case. We then used the given initial conditions to find the values of these constants.

Instead of using indefinite integrals, solve these equations by evaluating definite integrals with the appropriate initial condition as the lower integration limit, and the variable t, x, or t as the upper integration limit (remember, with definite integrals you don't need to include arbitrary integration constants). Show that you get the same results we found in class.