Bright Tutorials Bright Tutorials
ICSE Class 9 Physics Question 1 of 17

Motion in One Dimension — Question 15

Back to all questions
15
Question

Question 15

A car travels the first 25\dfrac {2}{5}th part of its total distance with a speed v1, and the remaining 35\dfrac {3}{5}th of the distance with speed v2. Its average speed is :

  1. 12v1v2\dfrac{1}{2}\sqrt{\text v_1 \text v_2}

  2. v1+v22\dfrac{\text v_1 +\text v_2}{2}

  3. 2v1v2v1+v2\dfrac{2\text v_1 \text v_2}{\text v_1 +\text v_2}

  4. 5v1v23v1+2v2\dfrac{5\text v_1 \text v_2}{3\text v_1 +2\text v_2}

Answer

5v1v23v1+2v2\dfrac{5\text v_1 \text v_2}{3\text v_1 +2\text v_2}

Reason — Let, total distance covered be S of which S1 is covered with v1 in time t1 and S2 with v2 in time t2.

Then,

S1=25S\text S_1=\dfrac{2}{5}\text S ............... (1)

and

S2=35S\text S_2=\dfrac{3}{5}\text S ............... (2)

As

Speed (v)=Distance (S)Time (t)\text {Speed (v)}=\dfrac{\text {Distance (S)}}{\text {Time (t)}}

Then,

⇒v1=S1t1⇒t1=S1v1\Rightarrow \text v_1=\dfrac{\text S_1}{\text t_1} \\[1 em] \Rightarrow \text t_1=\dfrac{\text S_1}{\text v_1}

Putting value of S1 from equation 1

⇒t1=25Sv1\Rightarrow \text t_1 = \dfrac{2}{5}\dfrac{\text S}{\text v_1}

Similarly

⇒v2=S2t2[1em]⇒t2=S2v2\Rightarrow \text v_2=\dfrac{\text S_2}{\text t_2} \\ [1 em] \Rightarrow\text t_2=\dfrac{\text S_2}{\text v_2}

Putting value of S2 from equation 2

⇒t2=35Sv2\Rightarrow\text t_2= \dfrac{3}{5}\dfrac{\text S}{\text v_2} Now,

Average Speed (v)=Total distance travelled (S)Total time taken (t)=St1+t2=S2S5v1+3S5v2=SS5(2v1+3v2)=SS5(2v2+3v1v1v2)=5v1v23v1+2v2\text {Average Speed (v)}=\dfrac{\text {Total distance travelled (S)}}{\text {Total time taken (t)}} \\[1 em] =\dfrac{\text S}{\text t_1 + \text t_2} \\[1 em] =\dfrac{\text S}{\dfrac{2\text S}{5\text v_1}+\dfrac{3\text S}{5\text v_2}} \\[1 em] = \dfrac{\text S}{\dfrac{\text S}{5}\Big(\dfrac{2}{\text v_1} + \dfrac{3}{\text v_2}\Big)} \\[1em] = \dfrac{\text S}{\dfrac{\text S}{5}\Big(\dfrac{2\text v_2 + 3 \text v_1}{\text v_1 \text v_2} \Big)} \\[1em] =\dfrac{5\text v_1 \text v_2}{3\text v_1 +2\text v_2}