In the above problem, find the time taken by the train to stop after the application of brakes. (80 s)
Difficulty: Medium
Solution:
by taking the data from problem 2.9:
Initial velocity = $V_{i} = 96 kmh^{-1}$ = $96 \times \frac{1000}{3600}$ =$\frac{96000}{3600} ms^{-1}$
Final velocity = $V_{f} = 0 ms^{-1}$
a =$(\frac{-48000}{3600})^{2}$ \times $\frac{3}{1600} ms^{-2}$
time = t =?
Or $V_{f}$ = $V_{i}$ + at
Or at = $V_{f} – V_{i}$
t = $V_{f} – V_\frac{_{i}}{a}$
t = $0 \frac{-48000}{3600}$-$(\frac{48000}{3600})$ \times $\frac{1}{1600}$
t = $\frac{-96000}{3600}\times$ $(\frac{3600}{48000})^{2}$ \times $\frac{1600}{3}$
t = $2\times \frac{48000}{3600}$\times $(\frac{3600}{48000}$\times $\frac{3600}{48000})$ \times $\frac{1600}{3}$
t = $2 \times \frac{3600}{3} \times 3$
t = $2\times 40$ = 80 s
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