A vehicle starts from rest and accelerates with a constant acceleration covering 200m in 5s. It then continues at a constant velocity for 300m before decelerating with a constant 2m/s^2 deceleration to a stop. What is the maximum speed attained, total time, and total distance covered?

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The maximum speed is the one the vehicle reaches at the end of the first part of its movement (with constant acceleration): [latex]v_{max}-v_{0}=a*t=\frac{2s-v_{0}*t}{t^{2}}*t[/latex] if [latex]v_{0}=0[/latex] then: [latex]v_{k}=\frac{2s}{t}=\frac{2*200m}{5s}=80\frac{m}{s}[/latex] Then it moves for 300m with 80[latex]\frac{m}{s}[/latex] velocity. It lasts for the time: [latex]t=\frac{300m}{80\frac{m}{s}}=3,75s[/latex] Finally it moves with the constant deceleration [latex]2\frac{m}{s^{2}}[/latex] The vehicle stops in time: [latex]t_{1}=\frac{v_{k}}{a_{d}}=\frac{80}{2}=40s[/latex] During those 40 seconds it moves for the distance of: [latex]s=\frac{a_{d}*t_{1}^{2}}{2}=1600m[/latex] Results: maximum speed: 80m/s, total time = 5 + 3,75 + 40 = 48,75 sek, distance covered = 200 + 300 + 1600 = 2100 m.

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