Starting from rest, a car takes T seconds to reach its cruising speed vmax. A plausible expression for the velocity as a function of time is vx1t2 = c vmax1 2t T - t 2 T2 2 t T vmax t T a. Demonstrate that this is a plausible function by drawing velocity and acceleration graphs. b. Find an expression for the distance traveled at time T in terms of T and the maximum acceleration a max. c. What are the maximum acceleration and the distance traveled for a car that reaches a cruising speed of 15 m/s in 8.0 s?

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