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Acceleration is a fundamental concept in physics that describes how quickly an object's velocity changes over time. It is given by the formula: \( a = \frac{\Delta v}{\Delta t} \), where \( \Delta v \) is the change in velocity and \( \Delta t \) is the change in time. In our problem, we calculated the sprinter's uniform acceleration using the equation of motion:

• \( s = ut + \frac{1}{2} a t^2 \) , where \( s \) is the displacement, \( u \) is the initial velocity, \( a \) is the acceleration, and \( t \) is the time.

Starting from rest means the initial velocity \( u = 0 \). By rearranging the equation, we can solve for \( a \):

• For the given problem: \( a = \frac{2s}{t^2} \).

This approach provides the sprinter's acceleration, helping us understand how fast the sprinter was speeding up over the 1.6 seconds. A uniform acceleration like this suggests a steady increase in speed.

Kinetic energy is the energy an object possesses due to its motion. It is calculated using the formula: \( KE = \frac{1}{2} m v^2 \), where \( m \) is the mass and \( v \) is the velocity. It's important to grasp that kinetic energy depends on both mass and the square of the velocity, meaning that it increases rapidly with higher speeds. In this scenario, we first determined the sprinter's mass from the given weight \( W = mg \), with \( g \approx 9.81 \, \mathrm{m/s^2} \), to find:

• \( m = \frac{W}{g} \).

Once we had the speed \( v \) from the previous calculation steps, substituting these values into the kinetic energy formula allowed us to find the energy the sprinter had at the end of the 1.6 seconds. Kinetic energy tells us how much work the sprinter can perform due to the motion.

Power in physics refers to the rate at which work is done or energy is transferred over time. The power generated by the sprinter can be calculated using the formula: \( P = \frac{\Delta KE}{t} \), where \( \Delta KE \) is the change in kinetic energy and \( t \) is the time taken. Power is measured in watts, with one watt equaling one joule per second. In this exercise, since the sprinter starts from rest, the initial kinetic energy is zero, and consequently, all the change in kinetic energy equals the final kinetic energy. By dividing this energy change by the time interval (1.6 seconds), we can find the average power generated by the sprinter during this interval. High power values indicate that the sprinter was able to exert a large amount of energy quickly, showcasing their explosive performance capability.

Equations of motion are crucial for analyzing and predicting the behavior of moving objects, especially when they are undergoing constant acceleration. These equations connect the core aspects of motion: displacement, initial velocity, final velocity, acceleration, and time. The primary equations include:

• \( v = u + at \) - relates velocity, initial velocity, acceleration, and time.
• \( s = ut + \frac{1}{2} a t^2 \) - connects displacement, initial velocity, acceleration, and time.
• \( v^2 = u^2 + 2as \) - links final velocity, initial velocity, acceleration, and displacement.

These equations allow for a comprehensive analysis of motion when an object accelerates at a constant rate. In our scenario, they were utilized to compute both the acceleration and final speed of the sprinter. It's important to ensure that all values are in coherent units, like meters, seconds, and meters per second, for consistent and accurate calculations.