Answer to Question #260547 in Molecular Physics | Thermodynamics for Noob

Question

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

Answer 1

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

$$d_1=v_0t+\dfrac{1}{2}at^2,$$ $$d_1=0+\dfrac{1}{2}\times2\ \dfrac{m}{s^2}\times(25\ s)^2=625\ m.$$

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:

$$d_{tot}=d_1+d_2+d_3=625\ m+1250\ m+417\ m=2292\ m.$$