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A particle starts from rest and moves in a straight line with constant acceleration passing through two points A and B which are 100m apart in 15s. If the velocity of the particle at B is three times it's velocity at A, find:
the velocity of the particle at A.
its acceleration
the distance of A from the starting point?
Most Upvoted Answer
A particle starts from rest and moves in a straight line with constant...
Given Information
- The distance between points A and B: 100 m
- Time taken to travel from A to B: 15 s
- Velocity at point B (vB) is three times the velocity at point A (vA).
Step-by-Step Solution
1. Calculate Average Velocity (v_avg)
- Average velocity from A to B = Total distance / Total time
- v_avg = 100 m / 15 s = 6.67 m/s
2. Express Velocities at A and B
- Since vB = 3 * vA, we can express v_avg in terms of vA:
- v_avg = (vA + vB) / 2 = (vA + 3vA) / 2 = 2vA
- Therefore, 2vA = 6.67 m/s → vA = 3.33 m/s
3. Find Velocity at B
- vB = 3 * vA = 3 * 3.33 m/s = 10 m/s
4. Determine Acceleration (a)
- Using the equation: vB = vA + at
- 10 m/s = 3.33 m/s + a * 15 s
- 10 - 3.33 = 15a → 6.67 = 15a
- Thus, a = 6.67 / 15 = 0.445 m/s²
5. Calculate Distance from the Starting Point to A (sA)
- Using the formula: sA = vA * t + (1/2) * a * t²
- The time to reach A (tA) can be calculated as: tA = t_total / 2 = 15 s / 2 = 7.5 s
- sA = 3.33 m/s * 7.5 s + 0.5 * 0.445 m/s² * (7.5 s)²
- sA = 24.975 m + 0.5 * 0.445 * 56.25 = 24.975 + 12.53 = 37.505 m
Summary
- Velocity at A (vA): 3.33 m/s
- Acceleration (a): 0.445 m/s²
- Distance of A from the starting point: 37.505 m
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A particle starts from rest and moves in a straight line with constant acceleration passing through two points A and B which are 100m apart in 15s. If the velocity of the particle at B is three times it's velocity at A, find:the velocity of the particle at A.its accelerationthe distance of A from the starting point?
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A particle starts from rest and moves in a straight line with constant acceleration passing through two points A and B which are 100m apart in 15s. If the velocity of the particle at B is three times it's velocity at A, find:the velocity of the particle at A.its accelerationthe distance of A from the starting point? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A particle starts from rest and moves in a straight line with constant acceleration passing through two points A and B which are 100m apart in 15s. If the velocity of the particle at B is three times it's velocity at A, find:the velocity of the particle at A.its accelerationthe distance of A from the starting point? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle starts from rest and moves in a straight line with constant acceleration passing through two points A and B which are 100m apart in 15s. If the velocity of the particle at B is three times it's velocity at A, find:the velocity of the particle at A.its accelerationthe distance of A from the starting point?.
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