Randall D. Knight — Kinematics in One Dimension: Problem Challenge_Problem_81

A good model for the acceleration of a car trying to reach top speed in the least amount of time is $a_x = a_0 - kv_x$, where $a_0$ is the initial acceleration and $k$ is a constant. a. Find an expression for $k$ in terms of $a_0$ and the car’s top speed $v_{max}$. b. Find an expression for the car’s velocity as a function of time. c. A MINI Cooper S has an initial acceleration of $4.0 \text{ m/s}^2$ and a top speed of $60 \text{ m/s}$. At maximum acceleration, how long does it take the car to reach 95% of its top speed?