Question

A student witnesses an 8.0-kilogram shopping cart undergoing uniform acceleration across a parking lot. It achieves a velocity of 4.0 meters per second in 0.5 seconds. What is the force's magnitude responsible for the acceleration of the shopping cart?

(1 point)
Responses

16.0 N
16.0 N

8.0 N
8.0 N

32.0 N
32.0 N

64.0 N

Answer 1

To find the force responsible for the acceleration of the shopping cart, we can use Newton's second law of motion, which states:

\[ F = m \cdot a \]

where:
- \( F \) is the force,
- \( m \) is the mass, and
- \( a \) is the acceleration.

First, we need to calculate the acceleration (\( a \)). We can use the formula for acceleration:

\[ a = \frac{\Delta v}{\Delta t} \]

where:
- \( \Delta v \) is the change in velocity,
- \( \Delta t \) is the change in time.

Given:
- Initial velocity (\( v_i \)) = 0 m/s (starting from rest),
- Final velocity (\( v_f \)) = 4.0 m/s,
- Time (\( \Delta t \)) = 0.5 seconds.

Now, we can calculate the acceleration:

\[
\Delta v = v_f - v_i = 4.0 \, \text{m/s} - 0 \, \text{m/s} = 4.0 \, \text{m/s}
\]

Now, inserting the values into the acceleration formula:

\[
a = \frac{4.0 \, \text{m/s}}{0.5 \, \text{s}} = 8.0 \, \text{m/s}^2
\]

Now that we have the acceleration, we can find the force using the mass of the shopping cart:

Given:
- Mass (\( m \)) = 8.0 kg.

Using the formula:

\[
F = m \cdot a = 8.0 \, \text{kg} \cdot 8.0 \, \text{m/s}^2 = 64.0 \, \text{N}
\]

Thus, the magnitude of the force responsible for the acceleration of the shopping cart is **64.0 N**.