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QuestionFind the speed of a train that travels 450 km450 \mathrm{~km} in 2.5 hours, expressed in m/s\mathrm{m/s}.

Studdy Solution

STEP 1

Assumptions1. The distance traveled by the train is450 km. The time taken by the train to cover this distance is.5 hours3. We need to find the speed in m/s4.1 km =1000 m5.1 hour =3600 seconds

STEP 2

First, we need to find the speed of the train in km/h. We can do this by dividing the distance by the time.
Speed=DistanceTimeSpeed = \frac{Distance}{Time}

STEP 3

Now, plug in the given values for the distance and time to calculate the speed.
Speed=450 km2.5 hoursSpeed = \frac{450\, km}{2.5\, hours}

STEP 4

Calculate the speed in km/h.
Speed=450 km2. hours=180 km/hSpeed = \frac{450\, km}{2.\, hours} =180\, km/h

STEP 5

Now that we have the speed in km/h, we need to convert it to m/s. We can do this by multiplying the speed by the conversion factor from km/h to m/s.
Speed=Speed in km/h×Conversion factorSpeed = Speed\, in\, km/h \times Conversion\, factor

STEP 6

The conversion factor from km/h to m/s is1000/3600, because there are1000 meters in a kilometer and3600 seconds in an hour.Conversion factor=1000 m3600 s=518Conversion\, factor = \frac{1000\, m}{3600\, s} = \frac{5}{18}

STEP 7

Now, plug in the values for the speed in km/h and the conversion factor to calculate the speed in m/s.
Speed=180 km/h×518Speed =180\, km/h \times \frac{5}{18}

STEP 8

Calculate the speed in m/s.
Speed=180 km/h×518=50 m/sSpeed =180\, km/h \times \frac{5}{18} =50\, m/sThe train's speed is50 m/s.

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