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An object starting from rest moves on a straight road for time t and comes to rest finally. The distant is converted in two parts. In first part it is accelerated at constant acceleration X and then deaccelerated at rate Y.Then what is the maximum vvelocit ?
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An object starting from rest moves on a straight road for time t and c...
Explanation of the problem
Given, an object starting from rest moves on a straight road for time t and comes to rest finally. The distance is converted into two parts. In the first part, it is accelerated at constant acceleration X and then deaccelerated at rate Y.
Finding the maximum velocity
The maximum velocity can be found using the following steps:
- Let the distance covered in the first part be d1 and the distance covered in the second part be d2.
- Using the first equation of motion, we can find the velocity after the first part of the motion:
- v = u + at
- v = 0 + Xt
- v = Xt
- Using the third equation of motion, we can find the time taken to cover the first part of the motion:
- s = ut + 1/2 at^2
- d1 = 0 + 1/2 X t^2
- t^2 = 2d1/X
- t = sqrt(2d1/X)
- Using the second equation of motion, we can find the final velocity after the second part of the motion:
- v^2 = u^2 + 2as
- v^2 = 0 + 2Yd2
- v = sqrt(2Yd2)
- Using the fourth equation of motion, we can find the time taken to cover the second part of the motion:
- s = ut + 1/2 at^2
- d2 = 0 + 1/2 Y t^2
- t^2 = 2d2/Y
- t = sqrt(2d2/Y)
- The total time taken for the motion is:
- total time = time taken in first part + time taken in second part
- total time = sqrt(2d1/X) + sqrt(2d2/Y)
- Therefore, the maximum velocity is:
- maximum velocity = distance/time
- maximum velocity = (d1 + d2)/(sqrt(2d1/X) + sqrt(2d2/Y))
Thus, the maximum velocity can be found using the above steps.
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An object starting from rest moves on a straight road for time t and c...
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An object starting from rest moves on a straight road for time t and comes to rest finally. The distant is converted in two parts. In first part it is accelerated at constant acceleration X and then deaccelerated at rate Y.Then what is the maximum vvelocit ?
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