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A body of mass 5 kg start from the origin with initial velocity u=(30i 40j)m/s if a constant force (-6i-5j)N acts on body the time in which y component of the velocity become zero is?
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A body of mass 5 kg start from the origin with initial velocity u=(30i...
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A body of mass 5 kg start from the origin with initial velocity u=(30i...
Given:
- Mass of the body, m = 5 kg
- Initial velocity, u = 30i + 40j m/s
- Constant force, F = -6i - 5j N
To find:
The time at which the y-component of velocity becomes zero.
Solution:
Step 1: Find the acceleration
The force acting on the body can be related to its acceleration using Newton's second law of motion:
F = ma
Given that F = -6i - 5j N and m = 5 kg, we can equate the force components to the respective components of acceleration:
-6 = 5a_x (Equation 1)
-5 = 5a_y (Equation 2)
Solving Equations 1 and 2, we find:
a_x = -6/5 m/s²
a_y = -1 m/s²
Step 2: Find the time
We know that acceleration is the rate of change of velocity with respect to time:
a = dv/dt
Since the acceleration is constant, we can integrate the above equation to find the velocity as a function of time:
∫dv = ∫adt
Integrating both sides, we get:
v = at + C
Where C is the constant of integration. Since the body starts from rest, the initial velocity (u) is equal to zero, so C = 0.
Therefore, the velocity as a function of time is given by:
v = at
Substituting the values of a_x and a_y, we get:
v_x = -6/5t
v_y = -t
Step 3: Find the time when the y-component of velocity becomes zero
To find the time at which the y-component of velocity becomes zero, we can equate v_y to zero and solve for t:
- t = 0
Therefore, the y-component of velocity becomes zero at t = 0.
Answer:
The time at which the y-component of velocity becomes zero is t = 0.
- Mass of the body, m = 5 kg
- Initial velocity, u = 30i + 40j m/s
- Constant force, F = -6i - 5j N
To find:
The time at which the y-component of velocity becomes zero.
Solution:
Step 1: Find the acceleration
The force acting on the body can be related to its acceleration using Newton's second law of motion:
F = ma
Given that F = -6i - 5j N and m = 5 kg, we can equate the force components to the respective components of acceleration:
-6 = 5a_x (Equation 1)
-5 = 5a_y (Equation 2)
Solving Equations 1 and 2, we find:
a_x = -6/5 m/s²
a_y = -1 m/s²
Step 2: Find the time
We know that acceleration is the rate of change of velocity with respect to time:
a = dv/dt
Since the acceleration is constant, we can integrate the above equation to find the velocity as a function of time:
∫dv = ∫adt
Integrating both sides, we get:
v = at + C
Where C is the constant of integration. Since the body starts from rest, the initial velocity (u) is equal to zero, so C = 0.
Therefore, the velocity as a function of time is given by:
v = at
Substituting the values of a_x and a_y, we get:
v_x = -6/5t
v_y = -t
Step 3: Find the time when the y-component of velocity becomes zero
To find the time at which the y-component of velocity becomes zero, we can equate v_y to zero and solve for t:
- t = 0
Therefore, the y-component of velocity becomes zero at t = 0.
Answer:
The time at which the y-component of velocity becomes zero is t = 0.
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A body of mass 5 kg start from the origin with initial velocity u=(30i 40j)m/s if a constant force (-6i-5j)N acts on body the time in which y component of the velocity become zero is?
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A body of mass 5 kg start from the origin with initial velocity u=(30i 40j)m/s if a constant force (-6i-5j)N acts on body the time in which y component of the velocity become zero is? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A body of mass 5 kg start from the origin with initial velocity u=(30i 40j)m/s if a constant force (-6i-5j)N acts on body the time in which y component of the velocity become zero is? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body of mass 5 kg start from the origin with initial velocity u=(30i 40j)m/s if a constant force (-6i-5j)N acts on body the time in which y component of the velocity become zero is?.
A body of mass 5 kg start from the origin with initial velocity u=(30i 40j)m/s if a constant force (-6i-5j)N acts on body the time in which y component of the velocity become zero is? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A body of mass 5 kg start from the origin with initial velocity u=(30i 40j)m/s if a constant force (-6i-5j)N acts on body the time in which y component of the velocity become zero is? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body of mass 5 kg start from the origin with initial velocity u=(30i 40j)m/s if a constant force (-6i-5j)N acts on body the time in which y component of the velocity become zero is?.
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