Calculate The Average Speed If You Run 40m In 10 Seconds

calculate The Average Speed If You Run 40m In 10 Seconds

Calculate the average speed if you run 40 meters in 10 seconds. Additionally, compute the average speed of a cheetah that runs 130 meters in 4 seconds. Determine the distance traveled if you maintain an average speed of 10 kilometers per hour for half an hour. Find the acceleration of a bus that goes from 10 kilometers per hour to a higher speed in 10 seconds. Assess the acceleration of an object on a distant planet that gains speed at a steady rate of 15 meters per second each second during free fall. Calculate the speed in meters per second of a snowboarder who accelerates from rest for 3 seconds down a ramp at an acceleration of 5 meters per second squared. Determine the vertical distance an object dropped from rest covers in 12 seconds of free fall. Find the maximum height of a ball thrown straight up with an initial speed of 30 meters per second and the total time it stays in the air, neglecting air resistance. Calculate the instantaneous velocity of a freely falling object 10 seconds after release and the average velocity during this interval. Also, determine the distance it falls in these 10 seconds. Finally, estimate how far raindrops would fall from a cloud 1 kilometer above the Earth's surface if there were no air drag, noting that in reality, air resistance affects falling rain drops.

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Understanding motion requires grasping fundamental concepts such as speed, velocity, acceleration, and displacement. These concepts allow us to analyze diverse scenarios ranging from a person running to objects falling on other planets, providing insights into the mechanics governing everyday phenomena and astronomical conditions.

Calculating Average Speed

The average speed is defined as the total distance traveled divided by the total time taken. For a runner covering 40 meters in 10 seconds, the calculation is straightforward:

Average Speed = Distance / Time = 40 m / 10 s = 4 m/s.

This indicates that the runner's average speed during the entire run is 4 meters per second.

Similarly, for a cheetah covering 130 meters in 4 seconds:

Average Speed = 130 m / 4 s = 32.5 m/s.

This reflects the cheetah's incredible speed, emphasizing the link between muscular power and rapid acceleration in animals adapted for sprinting.

Calculating Distance Traveled at a Constant Speed

If you maintain an average speed of 10 km/h for 0.5 hours, the distance traveled can be calculated by converting units into consistent SI units (meters and seconds). First, convert 10 km/h to meters per second:

10 km/h = (10,000 meters) / (3600 seconds) ≈ 2.78 m/s.

Then, multiply by the time in seconds:

Distance = Speed × Time = 2.78 m/s × 1800 s ≈ 500 meters.

This demonstrates how maintaining a moderate speed over time results in significant displacement.

Calculating Acceleration

For the bus accelerating from 10 km/h to a higher speed in 10 seconds, first convert the initial speed:

Initial speed = 10 km/h ≈ 2.78 m/s.

Assuming the final speed is not given, but generally, acceleration can be calculated if the final speed is known. If, for example, the bus reaches 30 km/h (8.33 m/s):

Final speed = 30 km/h ≈ 8.33 m/s.

Acceleration = (Final velocity - Initial velocity) / Time = (8.33 - 2.78) m/s / 10 s ≈ 0.555 m/s².

This indicates how quickly the bus increases its speed.

Object in Free Fall on a Distant Planet

On a distant planet, if an object gains speed at a steady rate of 15 meters per second each second during free fall, then the acceleration due to gravity (or the equivalent) is 15 m/s². This is independent of the planet's location because the rate of velocity change during free fall depends solely on gravitational acceleration, which varies from planet to planet.

Calculating Final Speed of an Accelerating Snowboarder

A snowboarder accelerating from rest (initial velocity = 0) at 5 m/s² for 3 seconds would reach a final velocity given by:

v = u + at = 0 + (5 m/s² × 3 s) = 15 m/s.

This illustrates how acceleration influences velocity over time in a real-world context.

Vertical Distance in Free Fall

For an object dropped from rest, neglecting air resistance, the displacement after time t can be found using the equation:

s = ½ gt².

Using g = 9.8 m/s² and t = 12 seconds:

s = 0.5 × 9.8 m/s² × (12)² = 0.5 × 9.8 × 144 = 705.6 meters.

This describes the vertical fall distance, emphasizing the acceleration due to gravity.

Projectile Motion and Maximum Height

A ball thrown vertically upward with an initial speed of 30 m/s reaches a maximum height where its velocity becomes zero. The height can be determined by:

h = (u²) / (2g) = (30)² / (2 × 9.8) ≈ 900 / 19.6 ≈ 45.92 meters.

The total time in the air is twice the time to reach maximum height:

t_total = 2 × u / g = 2 × 30 / 9.8 ≈ 6.12 seconds.

These calculations demonstrate the principles of kinematic equations in projectile motion.

Velocity and Displacement After 10 Seconds

For a freely falling object after 10 seconds:

  • Instantaneous velocity: v = gt = 9.8 m/s² × 10 s = 98 m/s downward.
  • Average velocity during this interval: v_avg = (initial velocity + final velocity) / 2 = (0 + 98) / 2 = 49 m/s.
  • Distance fallen: s = ½ gt² = 0.5 × 9.8 × 100 = 490 meters.

These values exemplify constant acceleration motion under gravity.

Distance Fallen Without Air Resistance

In the absence of air drag, a raindrop from a cloud 1 km above the surface of Earth would fall freely following the same principles, covering approximately 1000 meters. Under ideal conditions, neglecting air resistance, the fall time can be computed as:

t = √(2h/g) = √(2 × 1000 / 9.8) ≈ √204.08 ≈ 14.29 seconds.

This demonstrates the theoretical fall time assuming perfect free fall conditions.

Conclusion

The analyses across these various scenarios highlight key principles of physics, including the relationships between displacement, velocity, acceleration, and time. They also illustrate how different contexts — from terrestrial sports to planetary physics — are governed by the same fundamental laws. Understanding these concepts enables us to predict motion accurately and appreciate the complexities of dynamics in different environments.

References

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