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Rectilinear Kinematics with Piecewise Acceleration

Engineering Mechanics Dynamics · Engineering Mechanics — Dynamics (Rectilinear Kinematics)

Course: Engineering Mechanics Dynamics Book: Engineering Mechanics — Dynamics (Rectilinear Kinematics)

Question

A car is originally traveling at a velocity of 10 m/s when it is subjected to an acceleration defined by a piecewise function: - **Phase 1:** $a = 6$ m/s² (constant) for $0 \le t \le 15$ s - **Phase 2:** $a = 6 - 0.8(t - 15)$ m/s² (linearly decreasing) for $15 < t \le t'$ Initial conditions: $v(0) = 10$ m/s and $s(0) = 0$. Determine: 1. The car's maximum velocity $v_{\max}$. 2. The time $t'$ at which the car stops ($v = 0$).

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