GATE CE 2017 Set 1 — Question 44
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Engineering Mathematics → Calculus → Definite & Indefinite Integrals
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Question
A particle of mass 2 kg is travelling at a velocity of 1.5 m/s. A force (in N) is applied to it in the direction of motion for a duration of 2 seconds, where denotes time in seconds. The velocity (in m/s, up to one decimal place) of the particle immediately after the removal of the force is
Correct answer
5.4 to 5.6
Solution
Given:
Mass of the particle kg
Initial velocity m/s
Force applied N
Duration of force application to sAccording to the Impulse-Momentum Theorem, the impulse applied to the particle is equal to the change in its momentum:
Substitute the given values:
Integrate the force function:
Evaluate the definite integral:
Divide by 2:
Solve for the final velocity :
m/sThe velocity of the particle immediately after the removal of the force is m/s.The final answer is .
Mass of the particle kg
Initial velocity m/s
Force applied N
Duration of force application to sAccording to the Impulse-Momentum Theorem, the impulse applied to the particle is equal to the change in its momentum:
Substitute the given values:
Integrate the force function:
Evaluate the definite integral:
Divide by 2:
Solve for the final velocity :
m/sThe velocity of the particle immediately after the removal of the force is m/s.The final answer is .
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