Question

An object is moving along a number line, and its position in time is determined by a cubic function s(t), where time, t, is in seconds, and position, s, is in meters. The graph of s(t) is given below.

a. During what time interval(s) is the object moving in the negative direction of the number line?
A) 0 to 4 seconds
B) 8 to 12 seconds
C) 4 to 8 seconds
D) 12 to 16 seconds

Answer 1

The correct answer is option:

C) 4 to 8 seconds

Step-by-step explanation:

The object is moving in the negative direction of the number line when the function s(t) falls below the t-axis (where s(t) < 0). Looking at the graph between 4 to 8 seconds, the function dips below the t-axis, indicating negative positions along the number line during this time interval.

Before 4 seconds, the graph is entirely above the t-axis, suggesting positive positions, while after 8 seconds, the graph remains above the t-axis, indicating positive positions as well. Hence, the interval between 4 to 8 seconds corresponds to when the object moves in the negative direction along the number line.

Analyzing the graph's positioning concerning the t-axis helps identify the time intervals when the object's movement is in the negative direction, aiding in understanding the object's motion over time.