Question

A car travels total distance D. It travels half of this distance with the speed 40m/s and remaining half with 60m/s. Find the average speed

Answer 1

Answer:

Average speed = 48 m/s

Step-by-step explanation:

Given :

A car travels total distance D. It travels half of this distance with the speed 40m/s and remaining half with 60m/s.

To find :

the average speed

Solution :

Let t₁ be the time taken to cover the first half of the distance and t₂ be the time taken to cover the next half.

we know : Speed = distance covered/time taken

During the first half,

distance covered = D/2

speed = 40 m/s

$\sf time \ taken = \dfrac{\dfrac{D}{2}}{40} \\\\ \sf t_1 = \dfrac{D}{80} \ sec$

During the second half,

distance covered = D/2

speed = 60 m/s

$\sf time \ taken = \dfrac{\dfrac{D}{2}}{60} \\\\ \sf t_2 = \dfrac{D}{120} \ sec$

Average speed = total distance covered/total time taken

• total distance covered = D
• total time taken = t₁ + t₂

$\sf Average \ speed =\dfrac{D}{t_1+t_2} \\\\ \sf Average \ speed =\dfrac{D}{\dfrac{D}{80}+\dfrac{D}{120}} \\\\ \sf Average \ speed =\dfrac{D}{D\bigg(\dfrac{1}{80}+\dfrac{1}{120}\bigg)} \\\\ \sf Average \ speed =\dfrac{1}{\dfrac{1}{80}+\dfrac{1}{120}} \\\\ \sf Average \ speed=\dfrac{1}{\dfrac{3+2}{240}} \\\\\\ \sf Average \ speed=\dfrac{1}{\dfrac{5}{240}} \\\\\\ \sf Average \ speed=\dfrac{240}{5} \\\\ \implies \sf Average \ speed=48 \ m/s$