Question

4)A train travels at a speed of 58km/h for 0.5 hour ,46km/h for the next 0.25hour and then at 70km/h for the next 0.75 hour. Calculate the total distance covered by the train and its average speed.

Answer 1

Answer :

A train travels at a speed of 58km/h for 0.5h, 46km/h for the next 0.25h and then at 70km/h for the next 0.75h.

We have to find the total distance covered by the train and it's average speed$.$

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◈ Total distance covered by the train :

We know that speed is defined as the ratio of distance travelled to the time taken.

• Distance = Speed × Time

$\circ$ d = d₁ + d₂ + d₃

$\circ$ d = v₁t₁ + v₂t₂ + v₃t₃

$\circ\:\sf{d}=\sf{(58×0.5)+(46×0.25)+(70×0.75)}$

$\circ$ d = 29 + 11.5 + 52.5

$\circ$ d = 93 km

◈ Average speed of train :

Average speed of body is defined as the ratio of total distance travelled to the total time taken.

It is a scalar quantity having only magnitude.

SI unit : m/s

➝ Vav = d / (t₁ + t₂ + t₃)

➝ Vav = 93 / (0.5+0.25+0.75)

➝ Vav = 93/1.5

➝ Vav = 62 km/h

Answer 2

Answer:

• Total distance covered by Train = 93 km
• Average speed of Train = 62 km/h

Explanation:

Given,

• A train travels at a speed of 58 km/h for 0.5 hour, 46 km/h for next 0.25 hour and then at 70 km/h for next 0.75 hour

To find,

• Total distance covered by Train
• Average speed of train

so,

Using formula

• Distance = speed × time

Calculating Distance covered by train when it travels at 58 km/h for 0.5 hour

→ d₁ = 58 × 0.5

→ d₁ = 29 km

Calculating Distance covered by train when it travels at 46 km/h for 0.25 hour

→ d₂ = 46 × 0.25

→ d₂ = 11.5 km

Calculating Distance covered by train when it travels at 70 km/h for 0.75 hour

→ d₃ = 70 × 0.75

→ d₃ = 52.5 km

▶ Calculating total distance covered by the Train

→ d = d₁ + d₂ + d₃

→ d = 29 + 11.5 + 52.5

→ d = 93 km

therefore,

• Total distance covered by the Train is 93 km.

Now,

Using formula

• Average speed = total distance covered / total time taken

→ Average speed = ( 93 ) / ( 0.5 + 0.25 + 0.75 )

→ Average speed = 93 / 1.5

→ Average speed = 62 km/h

therefore,

• Average speed of Train is 62 km/h.