Question

3.3.2 test (cst): forces
question 3 of 20
which graph shows the change in velocity of an object in free fall?
a.
b.
c.
d.

Explanation:

Step1: Recall the formula for velocity in free - fall

The formula for the velocity of an object in free - fall is \(v = v_0+gt\), where \(v_0\) is the initial velocity (if the object is dropped from rest \(v_0 = 0\)), \(g\) is the acceleration due to gravity (\(g>0\)), and \(t\) is the time. This is a linear equation of the form \(y = mx + b\) (in this case \(y = v\), \(m = g\), \(x=t\), and \(b = v_0\)).

Step2: Analyze each graph

• Graph A: The velocity is decreasing over time. Since \(g>0\) and \(v = v_0+gt\) (for \(v_0\geq0\)), the velocity should increase (if \(v_0 = 0\)) or have a less negative slope (if \(v_0<0\) but in free - fall starting from rest \(v_0 = 0\)). So, graph A is incorrect.
• Graph B: The graph is a non - linear (exponential - like) curve. But \(v = v_0+gt\) is a linear equation. So, graph B is incorrect.
• Graph C: The velocity is constant over time. Since \(a=\frac{dv}{dt}=g

eq0\) (non - zero acceleration), the velocity cannot be constant. So, graph C is incorrect.

• Graph D: The graph is a straight line with a positive slope. When \(v_0 = 0\) (dropped from rest), \(v=gt\), which is a linear relationship between \(v\) and \(t\) with a positive slope \(g\).

Answer:

D.