Question

if a car cover ⅖th of dist with 10m/s and remaining dist with 30 m/s find avg speed​

Answer 1

Answer:

this is the answer ooookkkk

Answer 2

Answer:

Average speed = 16.66 m/s

Explanation:

In order to calculate the average speed of the car, we'll be using the formula of average speed. That is,

$\twoheadrightarrow \quad \sf {Speed_{(avg)} = \dfrac{Total \; Distance}{Total \; Time} }$

Let us assume the total distance covered as x.

⇒ Total distance = x

Now, we need to calculate the total time taken. In order to find it so, we need to calculate time taken in both cases.

According to the question,

• ⅖th of distance is covered with 10 m/s.

And,

• Remaining distance is covered with 30 m/s.

In first case :

⇒ Distance travelled $\sf (S_1)$ = ⅖x

⇒ Speed $\sf (V_1)$ = 10 m/s

So,

$\implies \quad \sf {Time= \dfrac{Distance}{Speed} }$

$\implies \quad \sf {T_1= \dfrac{S_1}{V_1} }$

$\implies \quad \sf {T_1= \dfrac{\cfrac{2}{5}x}{10} \; s }$

$\implies \quad \sf {T_1= \dfrac{2}{5}x \times \dfrac{1}{10} \; s }$

$\implies \quad \sf {T_1= \dfrac{1}{5}x \times \dfrac{1}{5} \; s }$

$\implies \quad \sf {T_1= \dfrac{1}{25}x \; s }$

In second case :

Now, in the second case, the remaining distance is covered with the speed of 30 m/s. So, remaining distance is the distance travelled in this case.

$\implies \sf {Distance_{(Remaining)} = Total \; distance - Distance_{(First \; case)} }$

$\implies \sf {Distance_{(Remaining)} = x - \dfrac{2}{5}x }$

$\implies \sf {Distance_{(Remaining)} = \dfrac{5x - 2x}{5} }$

$\implies \sf {Distance_{(Remaining)} = \dfrac{3x}{5}}$

So,

⇒ Distance travelled $\sf (S_2)$ = ⅗x

⇒ Speed $\sf (V_2)$ = 30 m/s

So,

$\implies \quad \sf {Time= \dfrac{Distance}{Speed} }$

$\implies \quad \sf {T_2= \dfrac{S_2}{V_2} }$

$\implies \quad \sf {T_2= \dfrac{\cfrac{3}{5}x}{30} \; s }$

$\implies \quad \sf {T_2= \dfrac{3}{5}x \times \dfrac{1}{30} \; s }$

$\implies \quad \sf {T_2= \dfrac{1}{5}x \times \dfrac{1}{10} \; s }$

$\implies \quad \sf {T_2= \dfrac{1}{50}x \; s }$

Therefore, total time will be given by,

$\implies \sf {Total \; Time = T_1 + T_2 }$

$\implies \sf {Total \; Time = \Bigg \{ \dfrac{1}{25}x + \dfrac{1}{50}x\Bigg \} \; s }$

$\implies \sf {Total \; Time = \Bigg \{ \dfrac{2x+1x}{50} \Bigg \} \; s }$

$\implies \sf {Total \; Time = \dfrac{3x}{50} \; s }$

Therefore, total time taken by the car is 3x/50 seconds.

Now, substituting values in the formula of average speed to find the average speed.

$\twoheadrightarrow \quad \sf {Speed_{(avg)} =\left \{ \dfrac{x}{\cfrac{3x}{50}} \right \} \; m/s}$

$\twoheadrightarrow \quad \sf {Speed_{(avg)} = \Bigg \{ x \times \dfrac{50}{3x}\Bigg \} \; m/s}$

$\twoheadrightarrow \quad \sf {Speed_{(avg)} = \Bigg \{ \dfrac{50}{3}\Bigg \}\; m/s }$

$\twoheadrightarrow \quad \bf\underline {Speed_{(avg)} = 16.66 \; m/s }$

Therefore, average speed of the car is 16.66 m/s.