a particle travels one-fourth of its journey with speed 20 m/s, then find the speed during remaining journey so that the average speed during complete journey is 32 m/s?
(1) 40 m/s
(2) 42 m/s
(3) 48 m/s
(4) 50 m/s
Answers
Given :-
◉ A particle travels one-fourth of its journey with speed 20 m/s
◉ Average speed = 32 m/s
To Find :-
◉ Speed in remaining journey
Solution :-
Let the total distance travelled throughout the journey be d.
It is given that, the particle travelled d/4 distance with speed 20 m/s
∴ Time taken = Distance / Speed
⇒ t₁ = (d / 4) / 20
⇒ t₁ = d/80 ...(1)
Now the remaining distance is:
⇒ d - d/4
⇒ 3d / 4
Let the speed at which the particle travelled in this remaining journey be x.
⇒ Time taken = Distance / Speed
⇒ t₂ = (3d/4) / x
⇒ t₂ = 3d / 4x ...(2)
Given in the question,
⇒ Average speed = 32 m/s
⇒ Total distance travelled / total time taken = 32
⇒ d / (d/80 + 3d/4x) = 32
⇒ d / ( [ dx + 60d ]/80x ) = 32
⇒ (d / 1) × (80x) / d(x + 60) = 32
⇒ 80x = 32x + 1920
⇒ 48x = 1920
⇒ x = 40 m/s
Hence, The speed in the remaining journey must be 40 m/s to make the average speed of the whole journey 32 m/s
∴ Option (1) is correct.
Answer:
the answer is 40 metre per second of the question A particle travels one fourth of its journey with speed 20 metre per second then find the speed during the remaining journey so that the average speed during the complete journey is 32