Driving your car, you start from rest, go a distance L = 105 m, and end up at rest once again. You want to determine the shortest time to accomplish this task (called the minimum-time problem). Your vehicle has a maximum acceleration capability of a1, and a maximum braking capability of az. After doing your research, you determine that the minimum-time solution is to accelerate at the maximum a value until time t₁, then decelerate at the maximum a2 value until the stopping time tą. Given values a1 = 7.5 m/s and a2 = -10 m/s, determine t₁, 12, and the car's maximum speed for this minimum-time acceleration profile.

Driving your car, you start from rest, go a distance L = 105 m, and end up at rest once again. You want to determine the shortest time to accomplish this task (called the minimum-time problem). Your vehicle has a maximum acceleration capability of a1, and a maximum braking capability of az. After doing your research, you determine that the minimum-time solution is to accelerate at the maximum a value until time t₁, then decelerate at the maximum a2 value until the stopping time tą. Given values a1 = 7.5 m/s and a2 = -10 m/s, determine t₁, 12, and the car's maximum speed for this minimum-time acceleration profile.

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