Can someone check my answer?
The change in the momentum of an object (Δ p) is given by the force, F, acting on the object multiplied by the time interval that the force was acting: Δ p = F Δt .
If the force (in newtons) acting on a particular object is given by F(t)=cost , what’s the total change in momentum of the object from time t = 5 until t = 7 seconds?
A) 0.402 newton•sec
B) 0.708 newton•sec <----
C) 0.909 newton•sec
D) 1.416 newton•sec
E) 1.616 newton•sec
integral f(t) dt from 5 to 7
sin 7 - sin 5 = .657 - .959 = -.30 if angle is in radians
or
.121 - .087 = .0347 if angle is in degrees
I suspect you left a pi out or something.
To find the total change in momentum of the object from t = 5 to t = 7 seconds, we need to integrate the force function F(t) = cost with respect to time, t, over the interval [5, 7].
The integral of cos(t) with respect to t is sin(t), so the integral of F(t) = cost with respect to t is sin(t).
To find the total change in momentum, we evaluate the integral of F(t) = cost from t = 5 to t = 7:
∫[5, 7] cost dt = sin(t) | [5, 7] = sin(7) - sin(5)
Now we can calculate the total change in momentum:
Δp = sin(7) - sin(5)
Using a calculator, sin(7) ≈ 0.656 and sin(5) ≈ -0.958, so the total change in momentum is:
Δp ≈ 0.656 - (-0.958) = 0.656 + 0.958 = 1.614
Therefore, the correct answer is E) 1.616 newton•sec.
To find the total change in momentum of the object from time t = 5 until t = 7 seconds, we need to integrate the force function, F(t)=cost, over the time interval [5, 7].
The integral of the force function with respect to time will give us the change in momentum: Δp = ∫F(t)dt.
To integrate the function F(t) = cost, we can use the power rule of integration. The power rule states that the integral of cos(t) with respect to t is sin(t), so we have: ∫cost dt = sin(t) + C, where C is the constant of integration.
Now, we can evaluate the integral over the time interval [5, 7]: Δp = ∫[5,7]cos(t)dt = [sin(t)] [5,7] = sin(7) - sin(5).
Using a calculator, we find that sin(7) - sin(5) is approximately 0.708.
Therefore, the total change in momentum of the object from time t = 5 until t = 7 seconds is approximately 0.708 newton·sec.
So, the correct answer is B) 0.708 newton·sec.