Question

do the math
express newtons second law
mathematically
the relationship of force (f), mass (m), and acceleration (a) can be expressed
mathematically with the equation f = ma, where force is in newtons (n), mass is in
kilograms (kg), and acceleration is in meters per second squared (m/s²). the table shows
ways that this equation can be rearranged to calculate one of the variables when you
know the other two.
three forms of newton’s second law
i want to know i know use this equation
acceleration (a) mass (m) and force (f) a = f/m
force (f) mass (m) and acceleration (a) f = ma
mass (m) force (f) and acceleration (a) m = f/a

1. complete the table for the equation a = f/m,

when m = 1 kg. then graph the points.
force (n) acceleration (m/s²)
0 0
1
2
3

1. how does this graph compare to the data you

graphed in the hands-on lab? how and why
might they differ?

Explanation:

Step1: Calculate acceleration for F=1N

Given \( a = \frac{F}{m} \) and \( m = 1 \, \text{kg} \), substitute \( F = 1 \, \text{N} \):
\( a = \frac{1}{1} = 1 \, \text{m/s}^2 \)

Step2: Calculate acceleration for F=2N

Substitute \( F = 2 \, \text{N} \) into \( a = \frac{F}{m} \):
\( a = \frac{2}{1} = 2 \, \text{m/s}^2 \)

Step3: Calculate acceleration for F=3N

Substitute \( F = 3 \, \text{N} \) into \( a = \frac{F}{m} \):
\( a = \frac{3}{1} = 3 \, \text{m/s}^2 \)

Answer:

The completed table is:

Force (N)	Acceleration (m/s²)
1	1
2	2
3	3

(For graphing, plot the points (0,0), (1,1), (2,2), (3,3) on a coordinate system with Force on the x - axis and Acceleration on the y - axis. The graph will be a straight line passing through the origin with a slope of 1, representing a direct proportionality between force and acceleration when mass is constant.)