# 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?

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.