Question

open response
analyze the following distance - time graphs. describe the motion of each. (2 points each)
(a)
(b)
(c)
a.

b.

c.

name:
date:
class period:

Explanation:

Step1: Analyze Graph (a)

In a distance - time graph, the slope represents speed. For graph (a), the distance (y - axis) remains constant as time (x - axis) increases. So, the object is at rest (speed = 0, since slope = $\frac{\Delta y}{\Delta x}=0$ as $\Delta y = 0$).

Step2: Analyze Graph (b)

Graph (b) is a straight line passing through the origin. The slope of the line is constant (since it's a straight line). The slope of a distance - time graph is speed ($v=\frac{\Delta d}{\Delta t}$). A constant positive slope means the object is moving with a constant speed (uniform motion).

Step3: Analyze Graph (c)

Graph (c) is a curve that is concave upwards. As time increases, the slope of the tangent to the curve (which represents the instantaneous speed) is increasing. This is because the rate of change of distance with respect to time (speed) is increasing. So, the object is moving with an increasing speed (accelerated motion).

Answer:

• For graph (a): The object is at rest (distance remains constant as time passes).
• For graph (b): The object is moving with a constant speed (uniform motion, as distance is directly proportional to time).
• For graph (c): The object is moving with an increasing speed (accelerated motion, as the rate of change of distance with time is increasing).