Question

the graph shows the motion of a car. which segments show that the car is accelerating? select three options.
a
b
c
d
e

Explanation:

To determine when a car is accelerating on a velocity - time graph, we use the concept that acceleration is the rate of change of velocity. Mathematically, \(a=\frac{\Delta v}{\Delta t}\). If the velocity of the object is changing (either increasing or decreasing, because deceleration is also a form of acceleration with a negative value), then the object is accelerating.

• Segment A: In this segment, as time increases from 0 to 1 second, the velocity of the car increases from 0 m/s to 30 m/s. Since there is a change in velocity (\(\Delta v> 0\)) over a non - zero time interval (\(\Delta t>0\)), the car is accelerating.
• Segment C: From around 5 to 6 seconds, the velocity of the car decreases from 40 m/s to 10 m/s. Here, \(\Delta v = 10 - 40=- 30\) m/s (negative change, which means deceleration, but deceleration is a type of acceleration). Since the velocity is changing, the car is accelerating.
• Segment D: From 7 to 8 seconds, the velocity of the car increases from 10 m/s to 40 m/s. With \(\Delta v=40 - 10 = 30\) m/s and \(\Delta t = 1\) second, the velocity is changing, so the car is accelerating.
• Segment B: In segment B (from 1 to 3 seconds), the velocity of the car remains constant at 30 m/s. So, \(\Delta v = 0\), and according to the formula for acceleration \(a = 0\), meaning the car is not accelerating.
• Segment E: From 9 to 10 seconds, the velocity of the car decreases from 40 m/s to 20 m/s. However, we are only choosing three options, and A, C, D are the ones that show a change in velocity (either increase or decrease) which indicates acceleration.

Answer:

A. Segment A, C. Segment C, D. Segment D