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.

Question

force(n) acceleration(m/s^2)
10 0.5
24 1.2
30 1.5
Based on the recorded observations, what is the mass of the go-cart in kilograms? (F=ma)

a
45 kg
b
28.8 kg
c
5 kg
d
20 kg

Answer 1

To find the mass of the go-cart using the relationship \( F = ma \) (where \( F \) is force, \( m \) is mass, and \( a \) is acceleration), we can rearrange the formula to solve for mass:

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

Let's use one of the data points to calculate the mass. We can use the first data point where \( F = 10 , \text{N} \) and \( a = 0.5 , \text{m/s}^2 \):

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

Now let's verify that this mass is consistent with the other data points.

For the second data point where \( F = 24 , \text{N} \) and \( a = 1.2 , \text{m/s}^2 \):

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

And for the third data point where \( F = 30 , \text{N} \) and \( a = 1.5 , \text{m/s}^2 \):

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

Since all three calculations give the same result, the mass of the go-cart is:

\[ \boxed{20 , \text{kg}} \]

Therefore, the correct answer is (d) 20 kg.