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In a bike race, bike P takes a time 't' less than bike Q at the finish and passes the finish point with a velocity 'V' more than the bike Q. Assuming that the bikes start from rest and travel with constant acceleration 'a¹' and 'a2', respectively then the value of V in terms of a1,a2 will be-.?
Verified Answer
In a bike race, bike P takes a time 't' less than bike Q at the finish...
Ans.
Method to Solve :
For A
acceleration=a1
total time=t'-t
final velocity=u+v
For B
acceleration=a2
total time=t'
final velocity=u
s=(1/2)a1(t'-t)^2=(1/2)a2(t')^2
therfor
1)(1-t/t')=(a2/a1)^(1/2)
also
(u+v)^2=2a1s
(u)^2=2a2s
dividing both we get
2)(1+v/u)=(a1/a2)^(1/2)
but u=a2t'
so substitute this value in 2 and put value of t' from 1
therefore we get
v=t(a1a2)^(1/2)
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Most Upvoted Answer
In a bike race, bike P takes a time 't' less than bike Q at the finish...
Explanation:
Given:
- Time taken by bike P = t
- Velocity of bike P at finish = V
- Acceleration of bike P = a1
- Acceleration of bike Q = a2
Key Points:
1. The time taken by bike P to finish is less than bike Q, therefore, bike P reaches the finish line before bike Q.
2. Bike P passes the finish line with a velocity V more than bike Q.
3. Both bikes start from rest and travel with constant acceleration.
Calculating the velocity of bike Q:
- Let the final velocity of bike Q be Vq.
- Using the equation of motion: Vq = a2 * t (since bike Q starts from rest)
- Therefore, Vq = a2 * t
Calculating the velocity of bike P:
- Using the equation of motion: V = a1 * t (since bike P starts from rest)
- Therefore, V = a1 * t
Relation between velocities of bike P and Q:
- V = Vq + V (since bike P passes the finish line with a velocity V more than bike Q)
- a1 * t = a2 * t + V
- V = a1 * t - a2 * t
- V = (a1 - a2) * t
Conclusion:
The value of V in terms of a1 and a2 is V = (a1 - a2) * t. This formula represents the difference in velocity between bike P and bike Q at the finish line.
Given:
- Time taken by bike P = t
- Velocity of bike P at finish = V
- Acceleration of bike P = a1
- Acceleration of bike Q = a2
Key Points:
1. The time taken by bike P to finish is less than bike Q, therefore, bike P reaches the finish line before bike Q.
2. Bike P passes the finish line with a velocity V more than bike Q.
3. Both bikes start from rest and travel with constant acceleration.
Calculating the velocity of bike Q:
- Let the final velocity of bike Q be Vq.
- Using the equation of motion: Vq = a2 * t (since bike Q starts from rest)
- Therefore, Vq = a2 * t
Calculating the velocity of bike P:
- Using the equation of motion: V = a1 * t (since bike P starts from rest)
- Therefore, V = a1 * t
Relation between velocities of bike P and Q:
- V = Vq + V (since bike P passes the finish line with a velocity V more than bike Q)
- a1 * t = a2 * t + V
- V = a1 * t - a2 * t
- V = (a1 - a2) * t
Conclusion:
The value of V in terms of a1 and a2 is V = (a1 - a2) * t. This formula represents the difference in velocity between bike P and bike Q at the finish line.
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In a bike race, bike P takes a time 't' less than bike Q at the finish and passes the finish point with a velocity 'V' more than the bike Q. Assuming that the bikes start from rest and travel with constant acceleration 'a¹' and 'a2', respectively then the value of V in terms of a1,a2 will be-.?
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In a bike race, bike P takes a time 't' less than bike Q at the finish and passes the finish point with a velocity 'V' more than the bike Q. Assuming that the bikes start from rest and travel with constant acceleration 'a¹' and 'a2', respectively then the value of V in terms of a1,a2 will be-.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about In a bike race, bike P takes a time 't' less than bike Q at the finish and passes the finish point with a velocity 'V' more than the bike Q. Assuming that the bikes start from rest and travel with constant acceleration 'a¹' and 'a2', respectively then the value of V in terms of a1,a2 will be-.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a bike race, bike P takes a time 't' less than bike Q at the finish and passes the finish point with a velocity 'V' more than the bike Q. Assuming that the bikes start from rest and travel with constant acceleration 'a¹' and 'a2', respectively then the value of V in terms of a1,a2 will be-.?.
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