Question

Example 8.2 The odometer of a car reads
2000 km at the start of a trip and
2400 kun at the end of the trip. If the
trip took 8 h, calculate the average
speed of the car in km h- and m s-1.​

Answer 1

Given :

• Distance at the start of the trip $\sf\:s_{1}$ = 2000 km

• Distance at the end of the trip $\sf\:s_{2}$ = 2400 km

• Time(t) = 8 hours

To Find :

• Average Speed of the car in km/hr and m/sec

Solution :

Distance covered by the car = $\sf\:s_{2} \: - \: s_{1}$

→ 2400 - 2000 km

→ 400 km

$\bigstar \: \boxed{ \sf \: Average \: Speed = \dfrac{Total \: Distance \: Covered }{Total \: Time \: taken }}$

$\longrightarrow \sf \: \cancel\dfrac{400}{8}$

$\longrightarrow \red{ \sf \: 50 \: km {h}^{ - 1} }$

Convert the unit in m/sec

[ For converting km/hr into m/sec we need to multiple the desired number with $\sf\frac{5}{18}$ ]

$\longrightarrow \sf \: 50 \times \dfrac{5}{18}$

$\longrightarrow \sf \cancel\dfrac{250}{18}$

$\longrightarrow \red{ \sf \: 13.9 \:m {s}^{ - 1} }$

$\therefore$ Average Speed of the car is 50 km/hr and 13.9 m/sec.

Answer 2

Given

Distance read by car at the start of trip = 2000 km.

Distance read by car at the end of trip = 2400 km.

Total time of trip = 8 hours.

To find

Average speed of car in km/h & m/s

Solution

Given that distance read₁ = 2000 km.

Distance read₂ = 2400 km.

So, distance covered = 2400 - 2000 = 400 km

We know that,

$\longrightarrow\underline{\boxed{\sf\blue{Average \: speed = \dfrac{Total \: distance}{Total \: time} }}}\: \star \\\\\longrightarrow\sf Av. speed = \dfrac{d_2 - d_1}{t_1 + t_2} \\\\\longrightarrow\sf Av. speed = \dfrac{2400 - 2000}{8}\\\\\longrightarrow\sf Av. speed = \dfrac{400}{8} \\\\\longrightarrow\underline{\boxed{\textsf{\textbf{Av. speed = 50 km/h }}}}\\\\\\\therefore\underline{\textsf{Average speed of car = {\textbf{50 km/h }}}}$

$\rule{200}{1}$

Here, distance = 400 km = 400 × 1000 = 400000 m

Time = 8 h = 8 × 3600 = 28800 s

Now using same formula we get :

$\longrightarrow\sf Av. speed = \dfrac{400000}{28800} \\\\\longrightarrow\underline{\boxed{\textsf{\textbf{Av. speed = 13.89 m/s}}}}\\\\\\\therefore\underline{\textsf{Average speed of car = {\textbf{13.89 m/s}}}}$