Question

In a series of controlled experiments, a student measures the force acting on a go-cart and the go-cart's acceleration. The student's data are shown below.
Force (N): 10, 24, 30
Acceleration (m/s^2): 0.5, 1.2, 1.5

Based on the recorded observations, what is the mass of the go-cart in kilograms? (F = ma)

A) 5 kg
B) 28.8 kg
C) 45 kg
D) 20 kg

Answer 1

To find the mass of the go-cart, we can use the formula \( F = ma \), where \( F \) represents the force applied, \( m \) is the mass, and \( a \) is the acceleration.

We can rearrange this formula to solve for mass:

\[
m = \frac{F}{a}
\]

Now, we can calculate the mass using the provided force and acceleration values. We will use any of the data pairs to find the mass.

Using the first data point:
- Force \( F = 10 \, \text{N} \)
- Acceleration \( a = 0.5 \, \text{m/s}^2 \)

Calculating the mass:

\[
m = \frac{F}{a} = \frac{10 \, \text{N}}{0.5 \, \text{m/s}^2} = \frac{10}{0.5} = 20 \, \text{kg}
\]

Now let's confirm this with the second and third data points for consistency.

Using the second data point:
- Force \( F = 24 \, \text{N} \)
- Acceleration \( a = 1.2 \, \text{m/s}^2 \)

Calculating the mass:

\[
m = \frac{F}{a} = \frac{24 \, \text{N}}{1.2 \, \text{m/s}^2} = \frac{24}{1.2} = 20 \, \text{kg}
\]

Using the third data point:
- Force \( F = 30 \, \text{N} \)
- Acceleration \( a = 1.5 \, \text{m/s}^2 \)

Calculating the mass:

\[
m = \frac{F}{a} = \frac{30 \, \text{N}}{1.5 \, \text{m/s}^2} = \frac{30}{1.5} = 20 \, \text{kg}
\]

In all cases, we find that the mass of the go-cart is \( 20 \, \text{kg} \).

Therefore, the answer is:

**D) 20 kg**