Question

A car is running with a speed of 56 kilometres per hour. Calculate the magnitude of speed in SI units​

Answer 1

Answer:

$\bf 15. \bar{5}$

Explanation:

As per the provided information in the given question, we have :

• A car is running with a speed of 56 km/h.

We are asked to calculate the magnitude of speed in SI units.

Before commencing the steps, let's first understand what is meant by speed. Speed is defined as distance travelled in per unit time. It is a scalar quantity, that means it requires both magnitude and direction for its description. SI unit of speed is m/s.

Now, according to the question, we have speed in km/h. We know that the SI unit of speed is m/s. So, we need to convert km/h to m/s, distance should be in metres unit and time should be in seconds unit.

$\longmapsto \rm { Speed = 56 \; kmh^{-1} }$

We can write it as,

$\longmapsto \rm { Speed = \dfrac{56 \; km}{1 \; h} }$

• 1 km = 1000 m
• 1 hour = 60 minutes

$\longmapsto \rm { Speed = \dfrac{56000 \; m}{60 \; min} }$

• 1 minute = 60 seconds

$\longmapsto \rm { Speed = \dfrac{56000 \; m}{(60\times 60 ) \; s} }$

$\longmapsto \rm { Speed = \dfrac{56000 \; m}{3600 \; s} }$

Cancelling the zeroes.

$\longmapsto \rm { Speed = \dfrac{560 \; m}{36 \; s} }$

Reducing it to the lowest terms.

$\longmapsto \rm { Speed = \cancel{ \dfrac{140 \; m}{9 \; s} }}$

$\longmapsto \bf { Speed = 15.\bar{5} \; ms^{-1} }$

∴ The magnitude of speed in SI unit is $\bf 15. \bar{5}$ m/s.

Easy Method :

We can also convert km/h into m/s by multiplying the value with 5/18 because 1 km/h is equivalent to 5/18 m/s.

$\longmapsto \rm { Speed = 56 \; kmh^{-1} }$

$\longmapsto \rm { Speed = \Bigg ( 56 \times \dfrac{5}{18} \Bigg ) \; ms^{-1} }$

$\longmapsto \rm { Speed = \Bigg ( 28 \times \dfrac{5}{9} \Bigg ) \; ms^{-1} }$

$\longmapsto \rm { Speed = \dfrac{140}{9} \; ms^{-1} }$

$\longmapsto \bf { Speed = 15.\bar{5} \; ms^{-1} }$

∴ The magnitude of speed in SI unit is $\bf 15. \bar{5}$ m/s.