Answer to Question #261379 in Molecular Physics | Thermodynamics for Noob

Question #261379

A bus starts from rest at a station and accelerates at a speed rate of 2m/s^2 for 15 seconds. It then runs at a constant speed for 25 seconds and slows down at -3m/s^2 until it stops. Find the total distance travelled by the bus.

1
Expert's answer
2021-11-07T19:29:27-0500

Let's first find the displacement of the bus when it accelerates:


"d_1=v_0t+\\dfrac{1}{2}at^2,""d_1=0+\\dfrac{1}{2}\\times2\\ \\dfrac{m}{s^2}\\times(15\\ s)^2=225\\ m."

Then, we can find the displacement of the bus when it runs at a constant speed:


"v=v_0+at=0+2\\ \\dfrac{m}{s^2}\\times25\\ s=50\\ \\dfrac{m}{s},""d_2=v_0t=50\\ \\dfrac{m}{s}\\times25\\ s=1250\\ m."

Let's find the time that the bus takes to stop:


"v=v_0+at,""t=\\dfrac{v-v_0}{a}=\\dfrac{0\\ \\dfrac{m}{s}-50\\ \\dfrac{m}{s}}{-3\\ \\dfrac{m}{s^2}}=16.7\\ s."

Then, we can find the displacement of the bus when it decelerates:


"d_3=v_0t+\\dfrac{1}{2}at^2,""d_3=50\\ \\dfrac{m}{s}\\times16.7\\ s+\\dfrac{1}{2}\\times(-3\\ \\dfrac{m}{s^2})\\times(16.7\\ s)^2=417\\ m."

Finally, we can find the total displacement travelled by the bus:


"d_{tot}=d_1+d_2+d_3=225\\ m+1250\\ m+417\\ m=1892\\ m."

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