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The rectilinear motion of a particle is given by s=v^2 - 9, where s is the displacement and v is the velocity When time t=0, s=0 and v=3m/s. Determine the s-t relation of motion
Ans) s=3t+0.25t^2?
Ans) s=3t+0.25t^2?
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The rectilinear motion of a particle is given by s=v^2 - 9, where s is...
Given:
s = v^2 - 9,
s = 0, v = 3m/s at t = 0
Required:
s-t relation of motion
Solution:
We know that acceleration is the derivative of velocity and velocity is the derivative of displacement. Hence, we can find the acceleration by differentiating the given equation with respect to time.
a = dv/dt = 2v(dv/ds)
We can substitute s = v^2 - 9 in the above equation to get:
a = 2v(dv/ds) = 2v(2v/2) = 2v^2
We know that acceleration is constant in this case as it is not a function of time. Hence, we can use the basic kinematic equation:
s = ut + 1/2 at^2
where u is the initial velocity and a is the constant acceleration.
Substituting the values, we get:
s = 3t + 1/2 * 2v^2 * t^2
s = 3t + v^2t^2
Substituting the given values, we get:
s = 3t + 0.25t^2
Hence, the s-t relation of motion is s=3t 0.25t^2.
Conclusion:
The rectilinear motion of a particle is given by s=v^2 - 9. The s-t relation of motion is s=3t 0.25t^2.
s = v^2 - 9,
s = 0, v = 3m/s at t = 0
Required:
s-t relation of motion
Solution:
We know that acceleration is the derivative of velocity and velocity is the derivative of displacement. Hence, we can find the acceleration by differentiating the given equation with respect to time.
a = dv/dt = 2v(dv/ds)
We can substitute s = v^2 - 9 in the above equation to get:
a = 2v(dv/ds) = 2v(2v/2) = 2v^2
We know that acceleration is constant in this case as it is not a function of time. Hence, we can use the basic kinematic equation:
s = ut + 1/2 at^2
where u is the initial velocity and a is the constant acceleration.
Substituting the values, we get:
s = 3t + 1/2 * 2v^2 * t^2
s = 3t + v^2t^2
Substituting the given values, we get:
s = 3t + 0.25t^2
Hence, the s-t relation of motion is s=3t 0.25t^2.
Conclusion:
The rectilinear motion of a particle is given by s=v^2 - 9. The s-t relation of motion is s=3t 0.25t^2.
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The rectilinear motion of a particle is given by s=v^2 - 9, where s is the displacement and v is the velocity When time t=0, s=0 and v=3m/s. Determine the s-t relation of motionAns) s=3t+0.25t^2?
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The rectilinear motion of a particle is given by s=v^2 - 9, where s is the displacement and v is the velocity When time t=0, s=0 and v=3m/s. Determine the s-t relation of motionAns) s=3t+0.25t^2? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The rectilinear motion of a particle is given by s=v^2 - 9, where s is the displacement and v is the velocity When time t=0, s=0 and v=3m/s. Determine the s-t relation of motionAns) s=3t+0.25t^2? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The rectilinear motion of a particle is given by s=v^2 - 9, where s is the displacement and v is the velocity When time t=0, s=0 and v=3m/s. Determine the s-t relation of motionAns) s=3t+0.25t^2?.
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