A car travels at 54km//h for first 20s,36km//h for next 30s and finally 18 km//h for next 10s. Find its average speed.

Convert to m/s: First, we need to convert the speeds from km/h to m/s because the time is given in seconds. To convert km/h to m/s, we divide by 3.6. 54 km/h = 54 / 3.6 m/s 36 km/h = 36 / 3.6 m/s 18 km/h = 18 / 3.6 m/sCalculate speeds: Now, let's calculate the speeds in m/s. 54 km/h = 15 m/s 36 km/h = 10 m/s 18 km/h = 5 m/sCalculate distances: Next, we calculate the distance covered at each speed. Distance = Speed × Time For the first speed: Distance1 = 15 m/s × 20 s For the second speed: Distance2 = 10 m/s × 30 s For the third speed: Distance3 = 5 m/s × 10 sPerform distance calculations: Now, let's perform the calculations for the distances. Distance1 = 15 m/s × 20 s = 300 m Distance2 = 10 m/s × 30 s = 300 m Distance3 = 5 m/s × 10 s = 50 mFind total distance: We add up the distances to find the total distance covered. Total distance = Distance1 + Distance2 + Distance3 Total distance = 300 m + 300 m + 50 mFind total time: Let's calculate the total distance. Total distance = 300 m + 300 m + 50 m = 650 mCalculate average speed: Now, we need to find the total time taken for the journey. Total time = Time1 + Time2 + Time3 Total time = 20 s + 30 s + 10 sLet's calculate the total time. Total time = 20 s + 30 s + 10 s = 60 sFinally, we calculate the average speed using the total distance and total time. Average speed = Total distance / Total time Average speed = 650 m / 60 sNow, let's perform the calculation for the average speed. Average speed = 650 m / 60 s ≈ 10.83 m/s

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Q. A car travels at

54\,\text{km/h}

for first

20\,\text{s}

36\,\text{km/h}

for next

30\,\text{s}

and finally

18\,\text{km/h}

for next

10\,\text{s}

. Find its average speed.

Convert to m/s: First, we need to convert the speeds from km/h to m/s because the time is given in seconds. To convert km/h to m/s, we divide by $3.6$ . $\newline$ $54 \, \text{km/h} = \frac{54}{3.6} \, \text{m/s}$ $\newline$ $36 \, \text{km/h} = \frac{36}{3.6} \, \text{m/s}$ $\newline$ $18 \, \text{km/h} = \frac{18}{3.6} \, \text{m/s}$
Calculate speeds: Now, let's calculate the speeds in m/s. $\newline$ $54$ km/h = $15$ m/s $\newline$ $36$ km/h = $10$ m/s $\newline$ $18$ km/h = $5$ m/s
Calculate distances: Next, we calculate the distance covered at each speed. $\newline$ Distance = Speed $\times$ Time $\newline$ For the first speed: $\newline$ Distance $_1$ = $15$ m/s $\times$ $20$ s $\newline$ For the second speed: $\newline$ Distance $_2$ = $10$ m/s $\times$ $30$ s $\newline$ For the third speed: $\newline$ Distance $_3$ = $_1$ $0$ m/s $\times$ $10$ s
Perform distance calculations: Now, let's perform the calculations for the distances. $\newline$ Distance $1$ = $15 \, \text{m/s} \times 20 \, \text{s} = 300 \, \text{m}$ $\newline$ Distance $2$ = $10 \, \text{m/s} \times 30 \, \text{s} = 300 \, \text{m}$ $\newline$ Distance $3$ = $5 \, \text{m/s} \times 10 \, \text{s} = 50 \, \text{m}$
Find total distance: We add up the distances to find the total distance covered. $\newline$ Total distance $= \text{Distance}_1 + \text{Distance}_2 + \text{Distance}_3$ $\newline$ Total distance $= 300 \, \text{m} + 300 \, \text{m} + 50 \, \text{m}$
Find total time: Let's calculate the total distance. $\newline$ Total distance = $300\,\text{m} + 300\,\text{m} + 50\,\text{m} = 650\,\text{m}$
Calculate average speed: Now, we need to find the total time taken for the journey. $\newline$ Total time $= \text{Time}_1 + \text{Time}_2 + \text{Time}_3$ $\newline$ Total time $= 20 \, \text{s} + 30 \, \text{s} + 10 \, \text{s}$
Calculate average speed: Now, we need to find the total time taken for the journey. $\newline$ Total time = Time $1$ + Time $2$ + Time $3$ $\newline$ Total time = $20 \, \text{s} + 30 \, \text{s} + 10 \, \text{s}$ Let's calculate the total time. $\newline$ Total time = $20 \, \text{s} + 30 \, \text{s} + 10 \, \text{s} = 60 \, \text{s}$
Calculate average speed: Now, we need to find the total time taken for the journey. $\newline$ Total time = Time $1$ + Time $2$ + Time $3$ $\newline$ Total time = $20 \, \text{s} + 30 \, \text{s} + 10 \, \text{s}$ Let's calculate the total time. $\newline$ Total time = $20 \, \text{s} + 30 \, \text{s} + 10 \, \text{s} = 60 \, \text{s}$ Finally, we calculate the average speed using the total distance and total time. $\newline$ Average speed = Total distance / Total time $\newline$ Average speed = $650 \, \text{m} / 60 \, \text{s}$
Calculate average speed: Now, we need to find the total time taken for the journey. $\newline$ Total time = Time $1$ + Time $2$ + Time $3$ $\newline$ Total time = $20 \, \text{s} + 30 \, \text{s} + 10 \, \text{s}$ Let's calculate the total time. $\newline$ Total time = $20 \, \text{s} + 30 \, \text{s} + 10 \, \text{s} = 60 \, \text{s}$ Finally, we calculate the average speed using the total distance and total time. $\newline$ Average speed = Total distance / Total time $\newline$ Average speed = $650 \, \text{m} / 60 \, \text{s}$ Now, let's perform the calculation for the average speed. $\newline$ Average speed = $650 \, \text{m} / 60 \, \text{s} \approx 10.83 \, \text{m/s}$