Question

1. (3 points) the figure shows a graph of the position x of two cars, c and d, as a function of time t. according to this graph, which statements about these cars must be true? (there could be more than one correct choice.) a) the magnitude of the acceleration of car c is greater than the magnitude of the acceleration of car d. b) the magnitude of the acceleration of car c is less than the magnitude of the acceleration of car d. c) at time t = 10 s, both cars have the same velocity. d) both cars have the same acceleration. e) the cars meet at time t = 10 s.

Explanation:

Step1: Recall position - time graph properties

In a position - time graph, the slope of the graph gives the velocity. A straight - line graph indicates a constant velocity (acceleration = 0), and a curved graph indicates non - zero acceleration.

Step2: Analyze the graphs of cars C and D

Car C has a straight - line graph, so its acceleration \(a_C=0\). Car D has a curved graph, so its acceleration \(a_D
eq0\).

Step3: Evaluate each option

• Option A: Since \(a_C = 0\) and \(a_D

eq0\), \(|a_C|\lt|a_D|\), so A is false.

• Option B: Since \(a_C = 0\) and \(a_D

eq0\), \(|a_C|\lt|a_D|\), so B is true.

• Option C: The slope of car C is constant and the slope of car D is changing. At \(t = 10\ s\), the slopes are not equal, so the velocities are not the same. C is false.
• Option D: Car C has zero acceleration and car D has non - zero acceleration. So they do not have the same acceleration. D is false.
• Option E: At \(t = 10\ s\), the two graphs intersect, which means the two cars are at the same position. So they meet at \(t = 10\ s\). E is true.

Answer:

B. The magnitude of the acceleration of car C is less than the magnitude of the acceleration of car D.
E. The cars meet at time \(t = 10\ s\).