Question

6. A body travels a distance of 10 km with a constant
speed of 30 km h- and then the next 40 km at a
constant speed of 50 kmh !. Find the average speed
for the whole journey.
13.​

Answer 1

Answer:

D1=10 km. T1=10/30=1/3hr. D2=40km.

Answer 2

TOPIC :- Motion in straight line

$\maltese\:\underline{\textsf{\textbf{AnsWer :}}}\:\maltese$

Given that,a body travels a distance of 10 km with a constant speed of 30 km/h :

• Distance (D₁) = 10 km
• Speed (S₁) = 30 km/hr

Also provided in the question that, The body travels a distance next 40 km at a constant speed of 50 km/h :

• Distance (D₂) = 40 km
• Speed (S₂) = 50 km/hr

We are asked to find the average speed. To calculate the average speed we will use the given below formula :

$\dag\: \underline{ \underline{\sf Average \: Speed \: (V_{av}) = \dfrac{Total \:distance}{Total \: time \: taken}}}$

Let's solve the question step by step :

$\longrightarrow\:\:\sf Average \: Speed = \dfrac{Total \: Distance}{Total \: time \: taken}$

$\longrightarrow\:\:\sf Average \: Speed = \dfrac{Distance (D_1) + Distance (D_2)}{\dfrac{Distance (D_1)}{Speed (S_1)} + \dfrac{Distance (D_2)}{Speed (S_2)}}$

Now, simply plug in the known values from the given :

$\longrightarrow\:\:\sf Average \: Speed = \dfrac{10+ 40}{ \dfrac{10}{30} +\dfrac{40}{50}}$

$\longrightarrow\:\:\sf Average \: Speed = \dfrac{50}{ \dfrac{1}{3} +\dfrac{4}{5}}$

$\longrightarrow\:\:\sf Average \: Speed = \dfrac{50}{ \dfrac{5 \times 1 + 4 \times 3}{3 \times 5}}$

$\longrightarrow\:\:\sf Average \: Speed = \dfrac{50}{ \dfrac{5 +12}{15}}$

$\longrightarrow\:\:\sf Average \: Speed = \dfrac{50}{ \dfrac{17}{15}}$

$\longrightarrow\:\:\sf Average \: Speed = \dfrac{50 \times 15}{17}$

$\longrightarrow\:\: \underline{ \boxed{\sf Average \: Speed = \dfrac{750}{17} \:km /hr }}$