Question

1. sketch the velocity - time graph for each motion. a. a city bus moving with constant velocity. b. an iguana that slows to rest at constant acceleration.

Explanation:

Step1: Recall velocity - time graph for constant velocity

For an object moving with constant velocity, the velocity does not change with time. So the velocity - time graph is a horizontal line. Let the velocity of the city bus be \(v_0\). The equation of the line is \(v = v_0\), where \(v\) is velocity and \(t\) is time.

Step2: Recall velocity - time graph for constant acceleration

The velocity - time relation for an object with constant acceleration \(a\) starting with an initial velocity \(v_0\) and coming to rest (\(v = 0\)) is given by \(v=v_0+at\). Since the iguana is slowing down, \(a<0\). It is a straight - line with a negative slope. When \(t = 0\), \(v = v_0\) and as \(t=\frac{-v_0}{a}\), \(v = 0\).

Answer:

a. A horizontal line on the velocity - time graph representing the constant velocity of the city bus.
b. A straight line with a negative slope on the velocity - time graph starting from an initial non - zero velocity and ending at zero velocity as the iguana comes to rest.