Answer :
Final answer:
The question is about the physics concepts of kinematics and energy. From initial and final velocities and the time duration, you calculate the acceleration. Using the work-energy theorem, you find the change in kinetic energy which represents work done, and in turn, utilize this to calculate the required power.
Explanation:
You are asking a question related to physics, more specifically, the topic of kinematics and energy.
In this scenario, first we need to calculate the work done. The work done (W) is a product of the mass (m), the acceleration (a), and the distance (d) traversed. In this case, the acceleration can be calculated using the formula a = Δv/t, where Δv is the change in velocity and t is the time. The change in velocity is 10.31 m/s - 5.51 m/s = 4.8 m/s. The time is 10 s, therefore, the acceleration is 4.8 m/s ÷ 10 s = 0.48 m/s².
The work done would then be the product of mass, acceleration, and distance; but since the distance is not given, we can't calculate work directly. Therefore we must use the work-energy theorem, which states that the work done is equal to the change in kinetic energy.
The change in kinetic energy (ΔKE) is 0.5*m*(v_f² - v_i²), where m is the mass, v_f is the final speed, and v_i is the initial speed. Plugging in the given values gives a ΔKE of about 37121 J.
Power (P) is the rate of doing work or the amount of energy transferred per unit time, and the formula is P = W/t. Here W is work done and t is time. When we plug our previously found values in, we get P = 37121 J/10 s = 3712.1 Watts.
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