Final answer:
The time Anthony pushed the cart can be calculated using Newton's second law of motion to find acceleration, followed by a kinematic equation to find time. However, there appears to be a misunderstanding in the question as negatime cannot be times, but correcting it gives a time of 1 second, which doesn't match the provided options.
Step-by-step explanation:
To find out how long Anthony pushed the cart, we need to calculate the acceleration of the cart and then use it to determine the time. The acceleration (a) can be found by using Newton's second law of motion, F=ma, where F is the net force applied, and m is the mass of the cart. After finding the acceleration, we use the kinematic equation v = u + at, where v is the final velocity, u is the initial velocity, and t is the time. Solving for t gives us the time Anthony pushed the cart.
First, we find the acceleration:
- Force (F) = 100 N
- Mass (m) = 20 kg
- Acceleration (a) = F/m = 100 N / 20 kg = 5 m/s2
Next, we use the kinematic equation:
- Initial velocity (u) = 3 m/s
- Final velocity (v) = 0 m/s (since the cart is removed)
- Acceleration (a) = 5 m/s2
Solving for time (t):
- v = u + at
- 0 = 3 + 5t
- 5t = -3
- t = -3 / 5
- t = -0.6 seconds
However, time cannot be negative, suggesting there might be a typo or misunderstanding in the question as it was presented. Since the question states that the front of the cart is 8 m/s, we might assume that the cart has been accelerated to 8 m/s, not removed at the velocity of 3 m/s. Let's correct this and proceed with v = 8 m/s:
- v = u + at
- 8 = 3 + 5t
- 5t = 8 - 3
- 5t = 5
- t = 5 / 5
- t = 1 second
Thus, the correct answer would then be that Anthony pushed the cart for 1 second to reach a velocity of 8 m/s; however, this time is not an option in the provided answers (A, B, C, D), indicating that there may be an error in the question.