General Science Motion and Free Fall

To find the total distance traveled, we add all segments of the journey together. The student walks 15 m north, then 9 m south, and finally 6 m east. The distance walked north and south is 15 m + 9 m = 24 m. Adding the 6 m walked east gives a total distance of 24 m + 6 m = 30 m. Thus, the total distance traveled by the student is 30 m.

Displacement measures the shortest distance from the initial position to the final position, considering direction. In this scenario, the cyclist first travels 20 m east and then returns 20 m west, ending up at the starting point. Since the starting and ending positions are the same, the total displacement is 0 m, indicating no net change in position despite the distance traveled.

To find the acceleration, we use the formula \( a = \frac{\Delta v}{\Delta t} \), where \( \Delta v \) is the change in velocity and \( \Delta t \) is the time taken. The runner starts from rest (initial velocity = 0 m/s) and reaches a final velocity of 12 m/s in 4 seconds. Thus, the change in velocity \( \Delta v = 12 \, \text{m/s} - 0 \, \text{m/s} = 12 \, \text{m/s} \). Plugging in the values, \( a = \frac{12 \, \text{m/s}}{4 \, \text{s}} = 3 \, \text{m/s}² \).

To calculate the distance a ball falls freely from rest, we use the formula for distance under constant acceleration: \( d = \frac{1}{2} g t^2 \). Here, \( g \) is the acceleration due to gravity (9.8 m/s²) and \( t \) is the time in seconds (5 seconds). Plugging in the values, we get \( d = \frac{1}{2} \times 9.8 \times (5^2) = \frac{1}{2} \times 9.8 \times 25 = 122.5 \) meters. Thus, the ball falls 122.5 meters in 5 seconds.

Displacement is a vector quantity, which means it has both magnitude and direction. It represents the shortest distance from an initial position to a final position, indicating not only how far an object has moved but also the direction of that movement. In contrast, scalar quantities only have magnitude and lack directional information. Therefore, stating that displacement is a scalar quantity is incorrect, as it fundamentally involves directional components.

To find the speed of the car, divide the total distance traveled by the total time taken. The car travels 180 km in 3 hours. Therefore, speed is calculated as 180 km ÷ 3 hours = 60 km/h. This indicates that the car maintains a consistent speed of 60 kilometers for every hour of travel.

Speed is a scalar quantity that measures how fast an object moves without regard to its direction. In contrast, velocity is a vector quantity that provides both the speed of the object and the direction of its motion. This distinction is crucial in physics, as it allows for a more comprehensive understanding of an object's movement, particularly when analyzing changes in direction or position over time. Thus, velocity inherently incorporates direction, while speed remains solely focused on the magnitude of movement.

When a basketball is thrown, it does not travel in a straight line due to the influence of gravity and the initial velocity imparted to it. This results in a curved trajectory, which is characteristic of curvilinear motion. Curvilinear motion refers to any motion along a curved path, distinguishing it from linear motion, where objects move in straight lines. The basketball's arc exemplifies how forces and initial angles combine to create this type of motion.

To find the final velocity of a stone dropped from rest after 6 seconds of free fall, we use the formula \( v = g \times t \), where \( g \) is the acceleration due to gravity (9.8 m/s²) and \( t \) is the time in seconds. Substituting the values, we get \( v = 9.8 \, \text{m/s²} \times 6 \, \text{s} = 58.8 \, \text{m/s} \). The direction is downward, as the stone is falling under the influence of gravity.