General Science Motion Forces Work and Energy

To find the total distance traveled, we add all the segments of the journey together. The student walks 12 m east, then 5 m west, which results in a net eastward distance of 7 m (12 m - 5 m). After this, the student walks 8 m north. The total distance is the sum of the distances in each direction: 12 m (east) + 5 m (west) + 8 m (north) = 25 m. Thus, the total distance traveled is 25 m.

To find the velocity of the cyclist, we use the formula for velocity, which is displacement divided by time. The cyclist travels 60 meters east in 10 seconds. Therefore, the velocity is calculated as 60 m / 10 s = 6 m/s. Since the direction of travel is east, the final velocity is expressed as 6 m/s east.

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 initial velocity is 4 m/s and the final velocity is 20 m/s, giving a change in velocity of \( 20 - 4 = 16 \) m/s. The time taken is 4 seconds. Thus, acceleration is calculated as \( a = \frac{16 \, \text{m/s}}{4 \, \text{s}} = 4 \, \text{m/s}² \).

To determine the distance a ball falls in free fall, we can use the formula: distance = 0.5 × g × t². Here, g (acceleration due to gravity) is 9.8 m/s² and t (time) is 3 seconds. Plugging in the values: distance = 0.5 × 9.8 m/s² × (3 s)² = 0.5 × 9.8 × 9 = 44.1 m. This calculation shows that after 3 seconds of free fall, the ball would have fallen 44.1 meters.

According to Newton's Second Law, the net force acting on an object is calculated using the formula \( F = m \times a \), where \( F \) is the net force, \( m \) is the mass, and \( a \) is the acceleration. In this case, the mass of the box is 6 kg and the acceleration is 3 m/s². Thus, the net force is \( 6 \, \text{kg} \times 3 \, \text{m/s}² = 18 \, \text{N} \). This calculation confirms that the net force acting on the box is 18 N.

Work is calculated using the formula: Work = Force × Distance. In this case, the student applies a force of 20 N over a distance of 5 m. By multiplying these values (20 N × 5 m), we find that the work done is 100 joules. This means that the effort exerted by the student in pushing the box results in a transfer of energy equivalent to 100 J.

Potential energy (PE) is calculated using the formula PE = mgh, where m is mass, g is the acceleration due to gravity, and h is height. For a 4 kg object at a height of 5 m, substituting the values gives PE = 4 kg * 9.8 m/s² * 5 m = 196 J. This indicates the energy stored due to its position above the ground, reflecting the work done against gravity to elevate the object.

Power is defined as the rate at which work is done, calculated using the formula: Power = Work / Time. In this case, the machine performs 500 joules of work in 10 seconds. By substituting the values into the formula, we get Power = 500 J / 10 s = 50 W. Therefore, the power output of the machine is 50 watts, indicating how much work is done per unit of time.