91Ó°ÊÓ

In physics, constant acceleration means that the acceleration of an object does not change over time. For the tennis ball in our problem, this occurs when the force from the racket makes the ball speed up at a uniform rate. Constant acceleration is a simplified scenario often used in physics to find how objects move when subjected to a steady force.

• Velocity changes at a steady rate.
• Helps in simplifying calculations by using linear equations.

Acceleration itself can be defined as the rate of change of velocity. In this problem, the tennis ball starts from rest, meaning it initially has zero velocity. It then quickly picks up speed, reaching a high velocity due to the constant acceleration exerted by the impact of the racket. This impact delivers energy to the ball uniformly over the distance it travels while in contact with the racket. That's the essence of constant acceleration: a steady increase in speed without fluctuations, making it predictable and easier to calculate.

The equations of motion are mathematical formulas that describe the relationship between an object's position, velocity, acceleration, and time. For an object like our tennis ball, they are crucial for determining various parameters of motion. The specific equation used in this problem is: \[ v^2 = u^2 + 2as \] where:

• \(v\) is the final velocity,
• \(u\) is the initial velocity,
• \(a\) is the acceleration,
• \(s\) is the distance covered while accelerating.

Given the initial and final velocities, and the distance, this equation allows us to solve for acceleration \(a\). It's why knowing the equations of motion is so valuable: they empower you to compute unknown variables by connecting all prominent aspects of motion. This approach is straightforward, given constant acceleration, making it perfect for scenarios like the tennis ball.

Newton's Second Law of Motion provides a simple yet profound explanation of net force. It defines net force as the total force acting on an object, quantified by the formula: \[ F = ma \] Here, \(F\) is the net force, \(m\) is the mass of the object, and \(a\) is the acceleration. In the context of our tennis ball, the net force is the force exerted by the racket, causing the ball's acceleration. - The net force is what changes the velocity of the ball.- It is the product of mass and the calculated acceleration. Understanding net force is key, as it helps in determining how quickly an object speeds up or slows down when acted upon by a force. In our exercise, by knowing the mass of the ball and its constant acceleration, we effortlessly used Newton’s second law to determine that the net force exerted on the ball is approximately 133.47 N. This real-world application of Newton's laws reveals how forces affect motion and helps us quantify those effects efficiently.