Question

question 6 (1 point)
which graph(s) represents a constant velocity?
a) a and c b) b and c
c) c d) a and b

Explanation:

• For a displacement - time graph, the velocity \(v=\frac{\Delta x}{\Delta t}\), which is the slope of the displacement - time graph.
• In graph a), the slope \(\frac{\Delta x}{\Delta t}=0\), so the velocity \(v = 0\) (a constant value, \(v=0\) is a special case of constant velocity).
• In graph b), the slope \(\frac{\Delta x}{\Delta t}\) is a non - zero constant. Let the equation of the line be \(x=mt + c\) (where \(m\) is the slope and \(c = 0\) in this case as it passes through the origin). Then \(v=\frac{dx}{dt}=m\) (constant).
• In graph c), the slope \(\frac{\Delta x}{\Delta t}\) is changing. If \(x\) is a non - linear function of \(t\) (e.g., \(x = at^{2}+bt + c\), \(a

eq0\)), then \(v=\frac{dx}{dt}=2at + b\) (a function of \(t\), not constant).

Answer:

d) a and b