Please help!

A young girl with mass 42.5kg is sliding on a horizontal, frictionless surface with an initial momentum that is due east and that has magnitude 94.0kg * (m/s) . Starting at 0s , a net force with magnitude F=( 8.10N/s )*t and direction due west is applied to the girl.

Part B
How much work has been done on the girl by the force in the time interval from t= 0s to the time calculated in part A?
Express your answer with the appropriate units.

Part C
What is the magnitude of the acceleration of the girl at the time calculated in part A?
Express your answer with the appropriate units.

To solve Part B and Part C, we need to first determine the time at which the net force is applied on the girl, which is denoted as t in the problem.

Part A states that the time calculated in Part A is the time at which the girl's momentum is reduced to half its initial value. To find this time, we can equate the initial and final momentum of the girl in the horizontal direction:

Initial momentum = final momentum
94.0 kg * (m/s) = 0.5 * 42.5 kg * vf

Solving for vf, the final velocity, we find vf = 2 * 94.0 kg * (m/s) / 42.5 kg = 4.451 kg * (m/s).

Now, we can calculate the time t at which the net force is applied by using the equation of motion:

vf = vi + at

where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time. Since the initial velocity in this case is zero (due to the girl sliding on a frictionless surface), we have:

4.451 kg * (m/s) = 0 + a * t

Solving for t, we find t = 4.451 kg * (m/s) / a.

Now we can proceed to Part B and Part C.

Part B: Work done on the girl by the force from t = 0s to the time calculated in Part A.
To find the work done, we can use the equation:

Work = Force * Distance

In this case, the force is given by F = (8.10 N/s) * t, and the distance is the displacement of the girl during this time interval. Since the force is applied in the opposite direction of the motion (due west), the displacement will be negative.

The displacement can be calculated using the equation of motion:

displacement = initial velocity * time + 0.5 * acceleration * time^2

For this problem, the initial velocity is zero (vi = 0), and we have already calculated the time t. We need to find the acceleration for Part C, which we will substitute in this equation to calculate the displacement.

Part C: Magnitude of acceleration of the girl at the time calculated in Part A.
To find the acceleration, we can use Newton's second law of motion:

Force = mass * acceleration

The force in this case is given by F = (8.10 N/s) * t, and the mass of the girl is 42.5 kg. Solving for acceleration, we get:

acceleration = Force / mass

Now, let's use these equations to find the answers to Part B and Part C.

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