Question

1. Draw the velocity-time graph of a car that starts with an initial velocity of 15km/hr and accelerates uniformly at 5ms-2 until it attains a maximum velocity of 50km/hr, it them maintains this speed for the next 2min. Use the graph to determine:

a. The total distance covered before it maintains the maximum velocity reached

b. The total distance covered in the entire journey

c. Average velocity

Answer 1

Let's first find the time that the car takes to attains a maximum velocity of 13.89 m/s:

$$v=v_0+at,$$ $$t=\dfrac{v-v_0}{a},$$ $$t=\dfrac{(50\ \dfrac{km}{h}-15\ \dfrac{km}{h})\times\dfrac{1000\ m}{1\ km}\times\dfrac{1\ h}{3600\ s}}{5\ \dfrac{m}{s^2}}=1.94\ s.$$

Let's draw the velocity versus time graph:

(a) We can find total distance covered before it maintains the maximum velocity reached from the area of small triangle under the graph:

$$d_1=\dfrac{1}{2}bh=\dfrac{1}{2}\times1.94\ s\times(13.89\ \dfrac{m}{s}-4.17\ \dfrac{m}{s})=9.43\ m.$$

(b) Let's first find the distance covered by the car for the next 2 min. It can be found from the area of rectangle under the graph:

$$d_2=ab=13.89\ \dfrac{m}{s}\times(121.94\ s-1.94\ s)=1667\ m.$$

Finally, we can find the total distance covered in the entire journey:

$$d_{tot}=d_1+d_2=9.43\ m+1667\ m=1676.43\ m.$$

(c) We can find the average velocity as follows:

$$v_{avg}=\dfrac{d_{tot}}{t_{tot}}=\dfrac{1676.43\ m}{121.94\ s}=13.75\ \dfrac{m}{s}.$$