Consider the time dependent velocity of the car shown in the figure below.
Consider the time-dependent velocity of the car shown in the figure below. (a) Use the graph of v(t) to write a piece-wise equation for v(t). (b) Calculate the acceleration a(t) for 0 lessthanorequalto t lessthanorequalto10 except for at times t = 1, 5, 8. Why are these points problematic? (c) Use anti-differentiation to find the equation for the position function x(t) for 0 lessthanorequalto t lessthanorequalto10. Use x(0) = 0 and continuity of x(t) to find the constants of integration. (d) Use your equation for x(t) to determine how far the car has traveled at t = 6 minutes. (e) How is the area under the graph of v(t) related to the answer in (d)? Explain.