Answer to Question #239552 in Electrical Engineering for may

Question #239552

Two runners are competing in a 400-meter dash. The first run at 6 m/s and maintains this speed. The second runner starts at 10 m/s and decelerates at 1/8 m/s2. Who will finish first? What will be their time difference?



1
Expert's answer
2021-09-21T07:09:17-0400

The time required for the first competitor to finish is


"t_1=\\frac D{v_1}=66.67\\text{ s}."

The time required for the second runner is


"D=v_2t_2-\\frac{at^2_2}2,\\\\\\space\\\\\nt_2^2\\frac a2-t_2v_2+D=0,\\\\\\space\\\\\nt_2=\\frac{v_2\\pm\\sqrt{v_2^2-2aD}}{a}=80\\text{ s}.\\\\\\space\\\\\n\\Delta t=t_2-t_1=13.33\\text{ s}."

The second runner will be 13.33 s behind the winner.


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