Question

define speed and explain what is meant by average speed. A motorist travels from a town A to a town B 145 distant in 3hours 45minutes find the average speed in kilometers per hour?

Answer 1

Appropriate Question:

Define speed and explain what is meant by average speed. A motorist travels from a town A to a town B 145 km distance in 3 hours 45 minutes. Find the average speed in km/h.

Explanation:

Speed is a physical quantity which can be defined as distance travelled per unit time. It is a scalar quantity and its SI unit is m/s. It is denoted by v.

Average speed is defined as total distance travelled divided by total time taken. Mathematically,

$\\ \longrightarrow \quad \boxed{\tt { Speed_{(Avg)} = \dfrac{Total \; distance}{Total \; time} } }$

In the 2nd part of the question, we have been given that,

• A motorist travels from a town A to a town B.
• Distance from A to B = 145 km
• Total time taken = 3 hours 45 minutes

Here, we need to convert 3 hours 45 minutes into hours, completely.

$\longrightarrow \tt { t = 3 \; h + 45 \; min }$

$\longrightarrow \tt { t = 3 \; h + \dfrac{45}{60}\; h }$

$\longrightarrow \tt { t = 3 \; h + \dfrac{9}{12}\; h }$

$\longrightarrow \tt { t = 3 \; h + \dfrac{3}{4}\; h }$

$\longrightarrow \tt { t = \dfrac{12 + 3}{4}\; h }$

$\longrightarrow \boxed{ \tt { t = \dfrac{15}{4}\; h }}$

As we know that,

$\\ \longrightarrow \boxed{\tt { Speed_{(Avg)} = \dfrac{Total \; distance}{Total \; time} } }$

$\longrightarrow \tt { Speed_{(Avg)} = \Bigg ( 145 \div \dfrac{15}{4} \Bigg ) \; kmh^{-1}}$

$\longrightarrow \tt { Speed_{(Avg)} = \Bigg ( 145 \times \dfrac{4}{15} \Bigg ) \; kmh^{-1}}$

$\longrightarrow \tt { Speed_{(Avg)} = \dfrac{580}{15} \; kmh^{-1}}$

$\longrightarrow \underline{\boxed{ \tt { Speed_{(Avg)} = 38.66 \; kmh^{-1}}} }\; \bigstar$

∴ The average speed of the motorist is 38.66 km/h.