Question

a car covers first 1000s of its distance with speed 18 km per hour and next 2000s if its distance with 36 km per hour then find its a erage speed for over all journey​

Answer 1

Given :-

$\sf\bullet\ Time_1(T_1)= 1000 seconds \\ \\ \sf\ \bullet Speed_1= 18km/h \\ \\ \sf\bullet \ Time_1(T_2 )= 2000 seconds \\ \\ \sf\bullet \ Speed_2= 36km/h$

To find:-

The average speed of whole journey

• Convert speed1 into m/s

$\sf\implies \ speed_1 = \cancel{18}\times \dfrac{5}{\cancel{18}} = 5m/s\\ \\ \implies\sf \ speed_2= \cancel{36}\times \dfrac{5}{\cancel{18}}\\ \\ \implies\sf speed_2= 2\times 5= 10m/s$

• Now find the distance1

$\implies\sf speed = \dfrac{Distance }{Time}\\ \\ \implies\sf 5= \dfrac{Distance }{1000}\\ \\ \implies\sf 5\times 1000 = Distance \\ \\ \implies\sf Distance_1 = 5000m$

$\boxed{\sf{\dag\ \ Distance (D_1)= 5000m }}$

• Now distance 2

$\implies\sf Speed =\dfrac{Distance }{Time}\\ \\ \implies\sf 10= \dfrac{Distance}{2000}\\ \\ \implies\sf 10\times 2000= Distance \\ \\ \implies\sf Distance_2 = 20,000m$

$\boxed{\sf{\dag\ \ Distance (D_2)= 20000m }}$

• Now find the average speed of whole journey !

$\bigstar{\boxed{\sf{ Average\ speed = \dfrac{Total \ distance }{Total \ time }}}}$

$\implies\sf Av.\ speed = \dfrac{D_1+D_2}{T_1+T_2}\\ \\ \implies\sf Av.\ speed = \dfrac{5000+20000}{1000+2000}\\ \\ \implies\sf Av.\ speed = \dfrac{25\cancel{000}}{3\cancel{000}}\\ \\ \implies\sf Av.\ speed = \cancel{\dfrac{25}{3}}\\ \\ \implies\sf Av.\ speed = 8.33m/s$

$\underline{\boxed{\textsf{\textbf{ \ Average \ speed \ of\ car = 8.33m/s}}}}$

Answer 2

Average speed of car for overall journey = 8.33 m/s

Solution

Correct Question :

A car covers part of it's distance in 1000 s with speed of 18 km/h and next part of distance in 2000 s with speed of 36 km/h. Find its average speed for overall journey.

We have time₁ = 1000 s, time₂ = 2000 s

Again, speed₁ = 18 km/h, speed₂ = 36 km/h

⇒ Speed₁ = 18 × (5/18) m/s

⇒ Speed₁ = 5 m/s

⇒ Speed₂ = 36 × (5/18) m/s

⇒ Speed₂ = 10 m/s

We know that,

● Speed = Distance/Time

⇒ 5 = Distance/1000

⇒ Distance = 5 × 1000

⇒ Distance₁ = 5000 m

Again,

⇒ 10 = Distance/2000

⇒ Distance = 2000 × 10

⇒ Distance₂ = 20000 m

Now we know that,

● Av. speed = Total distance/Total time

⇒Av. speed = (5000 + 20000)/(1000 + 2000)

⇒ Av. speed = 25000/3000

⇒ Av. speed = 25/3

⇒ Av. speed = 8.33 m/s

∴ Average speed of car = 8.33 m/s