a train starts from station P with uniform acceleration a1 for some distance and then goes with uniform retardation a2 for some more distance thookam rest at the station Q . the distance between the stations p and q is 4 kilometre and the train take 4 minutes to complete this journey if the acceleration in kilometre per hour unit show that
1/a1+1/a2=2
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Answers
Answer: According to the question , the train starts from a station P with uniform acceleration a1 for some distance , and after that for some more distance it goes with uniform retardation a2 to comes to rest at station Q .
Total distance = 4 km = 4000 m
Total time = 4 min = 240 sec
Our Target : 1/a1 + 1/a2
Let us take out ' 1/a1 ' and 1/a2
=> Let velocity be v1 time be t1 .
Applying equation of motion : v = u + at
»
-» a1 =
-» 1/a1 =
=> Let the velocity be v2 and time be t2
Again applying same equation :
But this time the train comes to rest i.e v2 = 0 and v1 = u2 .
»
-» 1/a2 =
Now we have both , 1/a1 and 1/a2 . But if wr add them , we will not get anything as we don't have the value of
So let us take out v1
Now , we will apply another equation of motion .
=> s = ut + 1/2 a*t^2
In this equation , u = 0 ( u1 = 0 , u2 = 0 )
=> s1 =
put the value of a1 in above equation i.e => a1 = v1/t1
-» s1 = 1/2 × v1 × t1
Similarly , s2 = 1/2 × v1 × t2
So , we will add these both , i.e ( s1 + s2 )
We know that s1 + s2 = 4000 m
also , t1 + t2 = 240 sec
=> 4000 = 1/2v1 ( t1 + t2 )
=> 4000 = 1/2 v1 ( 240 )
From this value of
Now finally , add those => 1/a1 and 1/a2
→ 1/a1 + 1/a2
→ t1/v1 + t2/v1
→
We have the values of t1+t2 and v1
=> t1 + t2 = 240
=> v1 = 33.33 m/s
-» 1/a1 + 1/a2 = (240)/(33.33)
Hope It Helps You.
Explanation:
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