Question

A car moves at a speed of 20 km/h for 15 minutes and then at a speed of 60 km/h for next 15 minutes. Calculate the total distance covered by the car.​

Answer 1

Required Answer:

$\large \dag$ Here, we are provided with speed of car in first 15 minutes is 20 km/h and for next 15 minutes is 60 km/h. We have to find out total distance covered by the car.

So, at first we'll calculate distance in both cases of first 15 minutes and of next 15 minutes and then sum of both distances will be total distance.

So, let's start to solve !!

Calculating distance in first 15 min :

Given:

• Time taken (t) = 15 minutes

→ 1 hour = 60 min

→ 1 min = $\sf {\dfrac{1}{60} \: hr }$

→ 15 min = $\sf {\dfrac{15}{60} \: hr }$

• Speed (v) = 20 km/h

Now, as we know that,

★ s = v × t

→ Distance = Speed × Time

→ s = 20 × $\sf {\dfrac{15}{60} }$ km

→ s = 2 × $\sf {\dfrac{15}{6} }$ km

→ s = $\sf {\dfrac{15}{3} }$ km

→ s = 5 km

Calculating speed in next 15 min :

Given:

• Time taken (t) = 15 minutes

→ 1 hour = 60 min

→ 1 min = $\sf {\dfrac{1}{60} \: hr }$

→ 15 min = $\sf {\dfrac{15}{60} \: hr }$

• Speed (v) = 60 km/h

Now, as we know that,

★ s = v × t

→ Distance = Speed × Time

→ s = 60 × $\sf {\dfrac{15}{60} }$ km

→ s = 6 × $\sf {\dfrac{15}{6} }$ km

→ s = 15 km

Therefore,

• Total distance covered = 15 km + 5 km
• Total distance covered = 20 km

Extra Information:

☛ Distance is defined as the total path covered by the body.

☛ SI unit of distance is metre(m).

☛ Distance is a scalar quantity.

☛ Formula :$\boxed{\sf{v \times t = s} }$

☛ Speed is defined as distance covered per unit time.

☛ SI unit of speed is m/s.

☛ Speed is a scalar quantity.

☛ Formula : $\boxed{\sf{v = \dfrac{s}{t} }}$

Answer 2

$\huge\red{\mid{\fbox{\texttt{Question}}}\mid}$

A car moves at a speed of 20 km/h for 15 minutes and then at a speed of 60 km/h for next 15 minutes. Calculate the total distance covered by the car.

$\huge\pink{\mid{\fbox{\tt{Answer}}\mid}}$

Total distance covered = 20km

$\huge\purple{\mid{\fbox{\tt{Solution}}\mid}}$

$\tt \green{GIVEN :}$

It is given that the car moved at a speed of 20km/hr for 15 minutes and then at a speed of 60km/hr for 15 minutes.

$\tt \blue {TO \: FIND : }$

the total distance covered by the car.

$\tt \orange{FORMULA \: USED : }$

☞ s = v × t

where ,

s = distance travelled by the car

v = speed of the car.

t = time taken by the car to travel the given distance

$\tt \purple {CALCULATIONS : }$

$\implies\sf60 min = 1 hour$

$\implies \sf1 min = \sf {\dfrac{1}{60} \: hr }$

$\implies\sf 15 min = \sf {\dfrac{15}{60} \: hr }$

[The above calculation is required because the time is always calculated in terms of hours if the distance is in km]

Calculating the distance covered by the car at a speed of 20km/hr

☞s = v × t

Substituting the values,

$\tt \implies \: s \: = 20 \times \frac{15}{60}$

$\tt \implies s = 20 \times { \cancel \frac{15}{60} }$

$\tt \implies \: s = 20 \times \frac{1}{4}$

$\tt \implies s = \cancel{20} \times \frac{1}{ \cancel{4}}$

$\tt \implies \: s = 5 \: km$

➙Now , Calculating the distance covered by car at a speed of 60km/hr.

☞s = v × t

substituting the values,

$\tt \implies \: s = 60 \times \frac{15}{60}$

$\tt \implies \: s = 60 \times { \cancel\frac {15}{60} }$

$\tt \implies \: s =60 \times \frac{1}{4}$

$\tt \implies \: s =\cancel{60} \times\frac{1} {\cancel4}$

$\tt \implies \: s =15km$

NOW, FOR FINDING THE TOTAL DISTANCE WE HAVE TO FIND THE DISTANCE COVERED BY THE CAR EACH TIME .

$\tt \pink{THEREFORE, }$

Total distance covered = sum of all distances travelled by the car

➙As we know, car travelled 5 km at a speed of 20km/hr and then travelled 15km at a speed of 60km/hr

HENCE,

Total distance covered = ( 5 + 15 )km

Total distance covered = 20 km