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A body is acted on by a force given by F = (10 + 2t) N. The impulse received by the body during the first four seconds is
- a)40 Ns
- b)56 Ns
- c)72 Ns
- d)32 Ns
Correct answer is option 'B'. Can you explain this answer?
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A body is acted on by a force given by F = (10 + 2t) N. The impulse re...
Impulse:
Impulse is the change in momentum of an object when it is acted upon by a force for a certain amount of time. Mathematically, impulse is given by the product of force and time.
Given:
Force, F = (10 2t) N
Time, t = 4 seconds
Finding Impulse:
To find the impulse received by the body during the first four seconds, we need to calculate the integral of the force with respect to time over the given time interval.
Integrating the force with respect to time, we get:
∫F dt = ∫(10 2t) dt
Simplifying the integral, we get:
∫F dt = 10t - t^2 + C
To find the constant of integration, C, we need to evaluate the integral at the lower limit of the time interval (t = 0) and set it equal to zero to account for the initial momentum being zero.
At t = 0, ∫F dt = 0
Therefore, 10(0) - (0)^2 + C = 0
C = 0
Substituting the value of C back into the integral, we get:
∫F dt = 10t - t^2
Now, we can evaluate the integral over the given time interval (t = 0 to t = 4):
∫F dt |[0, 4] = (10(4) - (4)^2) - (10(0) - (0)^2)
= (40 - 16) - (0 - 0)
= 24 Ns
Therefore, the impulse received by the body during the first four seconds is 24 Ns.
Answer:
The correct answer is option B) 24 Ns.
Impulse is the change in momentum of an object when it is acted upon by a force for a certain amount of time. Mathematically, impulse is given by the product of force and time.
Given:
Force, F = (10 2t) N
Time, t = 4 seconds
Finding Impulse:
To find the impulse received by the body during the first four seconds, we need to calculate the integral of the force with respect to time over the given time interval.
Integrating the force with respect to time, we get:
∫F dt = ∫(10 2t) dt
Simplifying the integral, we get:
∫F dt = 10t - t^2 + C
To find the constant of integration, C, we need to evaluate the integral at the lower limit of the time interval (t = 0) and set it equal to zero to account for the initial momentum being zero.
At t = 0, ∫F dt = 0
Therefore, 10(0) - (0)^2 + C = 0
C = 0
Substituting the value of C back into the integral, we get:
∫F dt = 10t - t^2
Now, we can evaluate the integral over the given time interval (t = 0 to t = 4):
∫F dt |[0, 4] = (10(4) - (4)^2) - (10(0) - (0)^2)
= (40 - 16) - (0 - 0)
= 24 Ns
Therefore, the impulse received by the body during the first four seconds is 24 Ns.
Answer:
The correct answer is option B) 24 Ns.
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A body is acted on by a force given by F = (10 + 2t) N. The impulse received by the body during the first four seconds is a)40 Ns b)56 Ns c)72 Ns d)32 Ns Correct answer is option 'B'. Can you explain this answer?
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