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