A body starting from rest accelerates uniformly at the rate of 10cm/s² and retards uniformly at the rate of 20cm/s². Find the least time in which it can complete the journey of 5km if the maximum velocity attained by the body is 72km/h
Answers
Given: A body starting from rest accelerates uniformly at the rate of 10 cm/s² and retards uniformly at the rate of 20 cm/s².
To find: the least time in which it can complete the journey of 5km.
Solution:
- Now we have given velocity as 72km/h, so changing it in m/s, we get:
72 km/hr = 20 m/s
- Now we have given acceleration as 10 cm/s², so changing it in m/s², we get:
10 cm/s² = 0.1 m/s²
- We have given retardation as 20 cm/s², so changing it in m/s², we get:
0.2 cm/s² = 0.2 m/s²
- Now the time taken for acceleration will be:
20 / 0.1 = 200 s
- Similarly, the time taken for retardation will be:
20 / 0.2 = 100 s
- Now we have given that body starts from rest, so u = 0.
- Now, s = ut + 1/2 x at², as u = 0 so, s = 1/2 x at²
- So, distance travelled while acceleration is:
d(1) = 1/2 x 0.1 x 200²
= 1/2 x 0.1 x 40000
= 2000 m
- Similarly, distance travelled while retardation is:
d(2) = 1/2 x 0.1 x 100²
= 1/2 x 0.1 x 10000
= 1000 m
- So the total distance is 3000 m.
- Now this distance will be travelled by car with 20 m/s as given in the question.
- So the time will be:
t = 3000 / 20 = 150 s
- So the total time will be: 200 + 100 + 150 = 450 s
Answer:
So, the least time in which it can complete the journey of 5km if the maximum velocity attained by the body is 72km/h is 450 seconds.
Answer:
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