Question

Salmon starts walking towards his home with a speed of 0.5m/s for first 10 minutes. Suddenly a dog starts to chase him so he runs at a speed of 4m/s for next 4 minutes and reaches home. Calculate Salmons average speed

Answer 1

Answer:

1.5 m/s

Explanation:

Formula to calculate average speed :

$\\ \longrightarrow \quad \pmb{\boxed{\sf {Speed_{(avg)} = \dfrac{Total \; distance}{Total \; time} }} }$

Finding total distance :

At first Salmon starts walking towards his home with a speed of 0.5m/s for first 10 minutes. That means, in first case :

• Speed of Salmon = 0.5 m/s
• Time taken by him = 10 minutes ⇒ 600 seconds

We need to calculate distance covered by him in those 10 minutes.

$\\ \longrightarrow \quad \pmb{\boxed{\sf {Distance \; (D_1) = Speed \times Time}} }$

$\\ \longrightarrow \sf{\quad { Distance \; (D_1) = (0.5 \times 600) \; m }}$

$\\ \longrightarrow \sf{\quad { Distance \; (D_1) =\Bigg (\dfrac{5}{10} \times 600 \Bigg ) \; m }}$

$\\ \longrightarrow \sf{\quad { Distance \; (D_1) = (5 \times 60) \; m }}$

$\\ \longrightarrow \bf{\quad \underline { Distance \; (D_1) = 300 \; m }}$

Therefore, in first 10 minutes, he covered 300 m.

After that, in next 4 minutes,

• Speed = 4 m/s
• Time = 4 minutes ⇒ 240 seconds

We need to calculate distance covered by him in next 4 minutes.

$\\ \longrightarrow \quad \pmb{\boxed{\sf {Distance \; (D_2) = Speed \times Time}} }$

$\\ \longrightarrow \sf{\quad { Distance \; (D_2) = (4 \times 240) \; m }}$

$\\ \longrightarrow \bf{\quad \underline { Distance \; (D_2) = 960 \; m }}$

Therefore, in next 4 minutes, he covered the distance of 960 m and then reached home. so, the total distance can be given by,

$\\ \longrightarrow \quad \pmb{\boxed{\sf {Total \; distance = D_1 + D_2}} }$

$\\ \longrightarrow \sf{\quad {Total \; distance = (300 +960) \; m }}$

$\\ \longrightarrow \bf{\quad \underline {Total \; distance = 1260 \; m }}$

Therefore, total distance covered in whole journey is 1260 m.

Finding total time :

Here,

$\longmapsto \bf {t_1 = 10 \; minutes \to 600 \; seconds }$

$\longmapsto \bf {t_2 = 4 \; minutes \to 240 \; seconds }$

$\\ \longrightarrow \quad \pmb{\boxed{\sf {Total \; time = t_1 + t_2}} }$

$\\ \longrightarrow \sf{\quad { Total \; time = (600 + 240) \; seconds}}$

$\\ \longrightarrow \bf{\quad \underline {Total \; time = 840 \; seconds }}$

Therefore, total time taken in the whole journey is 840 seconds.

Substituting the values of total distance and total time in the formula of average speed,

$\\ \longrightarrow \quad \pmb{\boxed{\sf {Speed_{(avg)} = \dfrac{Total \; distance}{Total \; time} }} }$

$\\ \longrightarrow \sf{\quad {Speed_{(avg)} = \dfrac{1260 \; m}{840 \; s} }}$

$\\ \longrightarrow \sf{\quad {Speed_{(avg)} = \dfrac{126 \; m}{84 \; s} }}$

$\\ \longrightarrow \bf{\quad \underline {Speed_{(avg)}= 1.5\; m s^{-1} }}$

Therefore, average speed of Salmon's is 1.5 m/s.