Let's analyze the questions in the image and solve them step by step:

Given:

• The cart is pulled with a force of 0.45 N.
• Initial velocity $v_0 = 0 \, \text{m/s}$.
• Time for which the force is applied, $t = 2.0 \, \text{s}$.
• Friction is not negligible.

We need to calculate several things based on this information.

i. Calculate the acceleration of the cart.

The force applied on the cart is given as 0.45 N, and using Newton's second law of motion:

$f = ma$

Where:

• $f = 0.45 \, \text{N}$ (force applied),
• $m$ is the mass of the cart (which isn't provided, but we may need to find or assume),
• $a$ is the acceleration (to be calculated).

To find the acceleration, we need to know the mass of the cart. If the mass was given, you would plug it into the formula to solve for $a$. For now, we leave this step open until we get the mass value.

ii. Calculate the cart’s velocity the moment the string breaks.

The cart is accelerating under a constant force until $t = 2.0 \, \text{s}$. Using the first equation of motion:

$v = v_0 + at$

Where:

• $v_0 = 0 \, \text{m/s}$ (initial velocity),
• $a$ is the acceleration from part (i),
• $t = 2.0 \, \text{s}$ (time for which the force is applied).

After finding the acceleration from part (i), you can substitute it here to find the velocity at $t = 2.0 \, \text{s}$.

iii. Calculate the new acceleration of the cart after the string breaks.

Once the string breaks, the cart will decelerate due to friction. The force due to friction will be the only force acting on the cart, and this force is opposing the motion. The deceleration can be found using the equation:

$f_{\text{friction}} = ma_{\text{new}}$

Where:

• $f_{\text{friction}}$ is the frictional force,
• $a_{\text{new}}$ is the deceleration (negative acceleration).

Again, the mass of the cart will be needed to calculate this. If friction is the only force, use the same equation as before but solve for the deceleration.

iv. Calculate the time it takes for the cart to stop after the string breaks.

Once the cart starts slowing down due to friction, we can use the following kinematic equation to find the time it takes to stop:

$v = v_0 + a_{\text{new}}t$

Here, $v = 0 \, \text{m/s}$ (since the cart comes to a stop), and $a_{\text{new}}$ is the deceleration calculated in part (iii). $v_0$ is the velocity at the moment the string breaks, found in part (ii).

If you have the mass or any other missing values, we can proceed to calculate each of these steps numerically. Let me know if you'd like further clarification or if you'd like to provide additional information!

Here are some related questions:

1. How does increasing the force affect the cart's acceleration?
2. How would the results change if friction were negligible?
3. What would happen to the cart's velocity if the string did not break?
4. How can the friction coefficient be calculated if the mass and deceleration are known?
5. How does time of applied force impact the final velocity of the cart?

Tip:

Always ensure that you have the correct units when applying Newton's laws. SI units (meters, kilograms, seconds) are usually the default, so check your values before solving equations.