Question

12 the graph shows the velocity of two different cars during a period of ten seconds. velocity-time graph graph omitted during which time interval is the acceleration of car 1 equal to zero relative to car 2? f 2 to 3 seconds g 4 to 5 seconds h 5 to 6 seconds j 9 to 10 seconds

Explanation:

To determine when the acceleration of Car 1 is equal to zero relative to Car 2, we need to find the time interval where the slopes (acceleration) of both cars' velocity - time graphs are equal (since relative acceleration \(a_{12}=a_1 - a_2\), and we want \(a_{12} = 0\) which means \(a_1=a_2\)). The slope of a velocity - time graph gives the acceleration.

Step 1: Analyze the slope of Car 1 and Car 2 in each interval

• Option F (2 - 3 seconds): Car 1's graph has a certain slope (acceleration) and Car 2's graph has a different slope (steeper), so their accelerations are not equal.
• Option G (4 - 5 seconds): Car 1's graph is a horizontal line (slope = 0, acceleration \(a_1 = 0\)) and Car 2's graph is also a horizontal line (slope = 0, acceleration \(a_2=0\)). So \(a_1=a_2\), which means the relative acceleration \(a_{12}=a_1 - a_2=0\).
• Option H (5 - 6 seconds): Car 1's graph has a slope of 0 (acceleration \(a_1 = 0\)) and Car 2's graph has a positive slope (acceleration \(a_2>0\)), so \(a_1

eq a_2\).

• Option J (9 - 10 seconds): Car 1's graph has a slope of 0 (acceleration \(a_1 = 0\)) and Car 2's graph has a positive slope (acceleration \(a_2>0\)), so \(a_1

eq a_2\).

Answer:

G. 4 to 5 seconds