Chapter 2: Problem 17

A car moves with a speed of \(60 \mathrm{~km} \mathrm{~h}^{-1}\) for \(20 \mathrm{~min}\) and then at a speed of \(30 \mathrm{~km} \mathrm{~h}^{-1}\) for the next \(20 \mathrm{~min}\). The total distance covered by the car is \(\mathrm{km} .\) (1) 10 (2) 20 (3) 30 (4) 40

Short Answer

Expert verified

Answer: The total distance covered by the car is 30 kilometers.

Step by step solution

Convert speeds to meters per minute

In the given problem, the speeds of the car are given in km/h. However, the time intervals are given in minutes. It is easier to work with the same units, so we will convert the speeds to the corresponding meters per minute. \(60 \mathrm{ ~km} \mathrm{ ~h}^{-1} = \frac{60}{60} \times 10^3~\text{meters per minute} = 1000 ~\mathrm{ m ~ min}^{-1}\) \(30 \mathrm{ ~km} \mathrm{ ~h}^{-1} = \frac{30}{60} \times 10^3 \text{meters per minute} = 500~ \mathrm{ m ~ min}^{-1}\).

Calculate the distance covered in each interval

Now, we will use the formula for distance - \(distance = speed × time\) for each interval to find the distances covered separately: Distance covered in the first interval: \(1000 ~\mathrm{ m ~ min}^{-1} \times 20~\text{min} = 20000~\text{m}\) Distance covered in the second interval: \(500 ~\mathrm{ m ~ min}^{-1} \times 20 ~\text{min} = 10000 ~\text{m}\)

Calculate the total distance covered

Now that we have the distances covered during each interval, we can just add them together to find the total distance covered by the car. Total distance covered = Distance in first interval + Distance in second interval = \(20000~\text{m} + 10000~\text{m} = 30000~\text{m}\) Since we need the distance in kilometers, we will convert the distance from meters to kilometers: \(30000~\text{m} = 30~\mathrm{ km}\) So, the total distance covered by the car is 30 kilometers, which corresponds to option (3).

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A car moves with a speed of \(60 \mathrm{~km} \mathrm{~h}^{-1}\) for \(20 \mathrm{~min}\) and then at a speed of \(30 \mathrm{~km} \mathrm{~h}^{-1}\) for the next \(20 \mathrm{~min}\). The total distance covered by the car is \(\mathrm{km} .\) (1) 10 (2) 20 (3) 30 (4) 40

Short Answer

Step by step solution

Convert speeds to meters per minute

Calculate the distance covered in each interval

Calculate the total distance covered

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