Question

1. A car travels 30 km at a uniform speed of 40
km/h and the next 30 km at a uniform speed of 20
km/h. Find its average speed.
k 30 km-* 30 km-
K
v;= 40 km/h
*
020 km/h​

Answer 1

Answer:

Step-by-step explanation:

According to the question,

                                       car travels 30 km at speed [u1] = 40 km/h

                                      car travels next 30 km at speed [u2] = 20 km/h

         we know that, time = distance/speed

            thus,                   time taken by car in first 30 km = 30/40=0.75 h

                                      time taken by car in next 30 km = 30/20=1.5 h

         we know that, average speed = total distance / total time

           thus,                         total distance = 30 + 30= 60 km

                                             total time = 0.75 + 1.5 = 2.25 h

                                          average speed = 60 / 2.25 = 26.6 km/h

           hence , the average speed of the car is 26.6 km/h

Answer 2

${\bold{\underline{\underline{Answer:}}}}$

${\bold{\therefore Avg.\:speed=\frac{80}{3}\:km/h}}$

${\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

• In the given question information given about a car travels 30 km at a uniform speed of 40 km/h and the next 30 km at a uniform speed of 20 km/h.

• We have to Find its average speed.

$\underline \bold{Given : } \\ \implies Initial \: speed( v_{i})= 40 \: kmh \\ \\ \implies Final \: speed( v_{f}) = 20 \: kmh \\ \\ \implies Distance(d_{1}) = 30 \: km \\ \\ \implies Distance(d_{2}) = 30 \: km\\\\\underline\bold{To\:Find:}\\\implies Avg.\:speed=?$

• According to given question :

$\bold{For \: first \: 30 \: km : } \\ \implies t_{i}= \frac{ d_{1}}{ v_{i} } \\ \\ \implies t_{i}= \frac{ 30}{40} \\ \\ \bold{\implies t_{i}= \frac{3}{4} \: hour} \\ \\ \bold{For \: next \: 30 \: km : } \\ \implies t_{f}= \frac{ d_{f}}{ v_{f}} \\ \\ \implies t_{f}= \frac{30}{20} \\ \\ \implies \bold{ t_{f}= \frac{3}{2} \: hour} \\ \\ \bold{For \: Avg .\: speed : } \\ \implies Avg. \: speed = \frac{Total \: distance}{Total \: time} \\ \\ \implies Avg. \: speed = \frac{ d_{i} + d_{f} }{ t_{i} + t_{f} } \\ \\ \implies Avg. \: speed = \frac{30 + 30}{ \frac{3}{2} + \frac{3}{4} } \\ \\ \implies Avg. \: speed = \frac{60}{9} \times 4 \\ \\ \bold{\implies Avg. \: speed = \frac{80}{3} \: km/ h}$