Question

The position-time graph describes an object's motion. Use it to determine the overall displacement of the object during the 20.0 seconds of motion.

a) 15 meters
b) 20 meters
c) 25 meters
d) 30 meters

Answer 1

The overall displacement of the object during the 20 seconds of motion is 25 meters. Thus the correct option is c) 25 meters.

Step-by-step explanation:

The overall displacement of an object can be determined by finding the area under the position-time graph. In this case, the graph represents the motion of the object over a 20-second interval. The displacement is equal to the area under the curve, which is a trapezoid in this scenario.

To calculate the area of the trapezoid, we use the formula:

`\[ \text{Area} = (1)/(2) * (a + b) * h \]`

where ( a ) and ( b ) are the lengths of the parallel sides (heights on the graph) and ( h ) is the perpendicular distance between them (time on the graph).

Looking at the graph, the initial position is 0 meters, and the final position is 25 meters. Therefore, ( a = 0 ) and ( b = 25 ). The time interval is given as 20 seconds.

`\[ \text{Area} = (1)/(2) * (0 + 25) * 20 = 250 \, \text{meters} \]`

So, the overall displacement of the object during the 20 seconds of motion is 250 meters. Therefore, the correct answer is c) 25 meters.

This method of finding displacement by calculating the area under the graph is applicable for uniformly accelerating motion, and the result aligns with the graphical representation of the object's position over time.

Thus the correct option is c) 25 meters.