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When an object accelerates uniformly, it means that its velocity changes at a constant rate over time. In real-life scenarios, like with our sprinter, uniform acceleration simplifies calculations because the change in speed happens evenly. In the given problem, the sprinter starts from rest with an initial velocity (\( u \)) of 0 and accelerates uniformly across 7 meters in 1.6 seconds. We use the formula \[ s = ut + \frac{1}{2} at^2,\]with \( s \) as the distance, \( u \) as the initial velocity, \( a \) as the acceleration, and \( t \) as the time. By solving this equation for \( a \), we can determine the sprinter's acceleration—revealing how the sprinter builds up speed quickly but steadily. This method is useful for describing motion where acceleration doesn't vary, such as cars moving straight on a flat road without changing gears, or objects in free-fall without air resistance.

Kinetic energy (\( KE \)) is the energy that an object possesses due to its motion. This energy depends on two factors: the mass of the object and its velocity. The formula to calculate kinetic energy is \[ KE = \frac{1}{2} mv^2,\]where \( m \) is mass and \( v \) is velocity. In our problem, the sprinter's mass is derived from his weight using the relation \( m = \frac{W}{g},\)where \( W \) is weight and \( g \) is the acceleration due to gravity (approximately 9.81 \( m/s^2 \)). Once we know the sprinter's mass and speed at 1.6 seconds, we can find his kinetic energy. This value shows how much energy the sprinter has due to his motion—helpful in understanding how energy transforms and is conserved during motion. The kinetic energy concept is widely applicable, from sports to analyzing car collisions and space travel.

Power is the rate at which work is done or energy is transferred. In simpler terms, it tells us how quickly energy is used. The average power generated by the sprinter can be determined by dividing the work done by the time taken, given by the equation \[ P = \frac{Work}{Time}.\]For the sprinter, the work done is equal to his change in kinetic energy over the 1.6-second timeframe. Calculating average power helps us understand how efficiently and effectively sprinters expend energy. For engineers and athletes alike, power is a key concept—it can indicate performance efficiency, the design of engines, and much more. For instance, upgrading the engine of a car to increase its power output means the car can accelerate faster, reaching desired speeds in shorter times.In our sprinting example, high average power tells of a significant transformation of stored energy into kinetic energy, showcasing the sprinter’s explosive physical ability.