Final answer:
The force required to accelerate a 2.00-kg object from 2.50 m/s to 8.00 m/s over a distance of 1.80 m is determined by using the work-energy principle and calculating the change in kinetic energy.
Step-by-step explanation:
To determine the force required to accelerate a 2.00-kg object from 2.50 m/s to 8.00 m/s over a distance of 1.80 m, we can use the work-energy principle. This principle states that the work done on an object is equal to the change in kinetic energy. The work done by the force (W) can be calculated as W = Fd, where F is the force and d is the distance over which the force is applied.
The kinetic energy (KE) of an object is given by KE = 0.5 * m * v^2, where m is the mass and v is the velocity of the object. The change in kinetic energy (ΔKE) is then ΔKE = KE_final - KE_initial = 0.5 * m * (v_final^2 - v_initial^2).
Setting the work done equal to the change in kinetic energy, we get F * d = 0.5 * m * (v_final^2 - v_initial^2). Plugging in our values: F * 1.80 m = 0.5 * 2.00 kg * (8.00^2 - 2.50^2) m^2/s^2. Solving for F gives us the required force.