Significant Figures and Kinematics Basics

The measurement 4.500 m contains four significant figures. In this context, all non-zero digits are significant, as well as any zeros that are between them or trailing zeros in a decimal number. The digits '4', '5', '0', and the trailing '0' after the decimal point are all counted as significant, leading to a total of four significant figures.

Significant figures refer to the digits in a number that contribute to its accuracy and precision. This includes all non-zero digits, any zeros between significant digits, and trailing zeros in a decimal number. They reflect the certainty of the measurement and help convey how precise a measurement is. Therefore, understanding significant figures is essential in scientific calculations and reporting results accurately.

To convert 2.5 hours to seconds, first convert hours to minutes by multiplying by 60, giving 150 minutes. Next, convert minutes to seconds by multiplying by 60 again, resulting in 9,000 seconds. When expressed in scientific notation with two significant figures, 9,000 becomes 9.0 × 10³ s. This notation highlights the precision of the measurement while adhering to the significant figures rule.

To find the total distance traveled, you simply add the distances covered in each direction. The person first travels 180 meters north and then 65 meters south. The total distance is calculated as 180 m + 65 m, which equals 245 m. It’s important to note that total distance is the sum of all movement, regardless of direction, not the net displacement.

Displacement is the shortest distance from the initial to the final position, taking direction into account. In this scenario, the person travels 180 m north and then 65 m south. To find the net movement, subtract the distance traveled south from the distance traveled north: 180 m - 65 m = 115 m. Since the final position is still north of the starting point, the displacement is 115 m north.

Displacement refers to the shortest distance from the initial position to the final position, along with the direction. In this scenario, the student completes a full lap of 400 meters and returns to the starting point. Since the starting and ending positions are the same, the overall change in position is zero. Therefore, the displacement, which measures this change, is 0 meters, confirming that the statement is true.

Displacement is a vector quantity, which means it has both magnitude and direction. Unlike scalar quantities that only consider size, displacement describes the shortest distance from the initial to the final position, incorporating the direction of that movement. For example, moving 5 meters east and 5 meters west results in zero displacement, highlighting the importance of direction in its definition. Thus, the statement that displacement is a scalar quantity is incorrect.

To convert meters to centimeters, you multiply by 100, since 1 meter equals 100 centimeters. Therefore, 4.500 meters is calculated as 4.500 × 100 = 450.0 centimeters. When preserving four significant figures, the result retains the decimal point and the trailing zero, indicating precision in measurement. Thus, 4.500 m is equal to 450.0 cm, maintaining the specified number of significant figures.

When the student runs one complete lap around a 400-meter track, they cover the entire length of the track from the starting point and return to the same point. The distance traveled is the total path covered during the run, which is the circumference of the track. Since the student completes one full lap, the distance traveled is 400 meters, regardless of their starting and ending position being the same.