Question

a car start from the rest accelerate at the rate of f through a distance s then continue at constant speed for time t and then at the rate f/2 to come to rest if the total distance travelled is 5s,then

Answer 1

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Answer 2

Answer:

Question:-

1. A car, starting from rest, accelerates at the rate (f) through a distance (S), then continues at constant speed for some time (t) and then decelerates at the rate ` f//2` to come to rest. If the total distance is 5s, then prove that $\rm S=\frac{1}{2} /ft^{2}$

Solution:-

━☆ $\rm v^{2}=u^{2} + 2as$

━☆ $\rm v_1^{2} = 0+2 \times f \times s$

━☆ $\rm v_1 = \sqrt{2fs}$

━☆ $\rm v^{2}= u^{2} +2as$

━☆ 0 = $\rm v_1^2-2 \times\frac{f}{2} \times (CD)$

━☆ f [CD] = 2fs

━☆ CD = 2s

━☆ $\rm v_1=\frac{BC}{t}$

━☆ $\rm BC^{2} {V_1 t}$

━☆ $\rm BC= \sqrt{2fs \times t}$

            AB + BC + CD = 5s

━☆ $\rm S+(\sqrt{2fs} )t+2s=5s$

━☆ $\rm (\sqrt{2fs} )t = 2s$

━☆ $\rm 2fs \times t^{2} = 4s^{2}$

  Answer ━☆ $\rm S= \frac{1}{2} ft^{2}$

            $\huge\bold{Proved!}$