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12 Nov 2019
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.
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.
Nestor RutherfordLv2
23 Mar 2019