8. A400 hp engine in a 1,600 kg car applies maximum force for 2 seconds to accelerate the car onto the interstate. It the car moves at 8m/s before accelerating, what is its speed after the 2 seconds of acceleration?

To solve this problem, we need to use the principles of Newton's laws of motion and the equations of motion.<br /><br />Given information:<br />- The engine has a power output of 400 hp.<br />- The car has a mass of 1,600 kg.<br />- The car is initially moving at a speed of 8 m/s.<br />- The engine applies maximum force for 2 seconds to accelerate the car.<br /><br />Step 1: Calculate the force applied by the engine.<br />Power = Force × Velocity<br />400 hp = Force × Velocity<br />Force = 400 hp / Velocity<br /><br />Since the engine is applying maximum force, we can assume the velocity is at its maximum value, which is 8 m/s.<br />Force = 400 hp / 8 m/s = 50,000 N<br /><br />Step 2: Calculate the acceleration of the car.<br />Force = Mass × Acceleration<br />50,000 N = 1,600 kg × Acceleration<br />Acceleration = 50,000 N / 1,600 kg = 31.25 m/s²<br /><br />Step 3: Calculate the final speed of the car after 2 seconds of acceleration.<br />Initial velocity (u) = 8 m/s<br />Acceleration (a) = 31.25 m/s²<br />Time (t) = 2 seconds<br /><br />Final velocity (v) = u + a × t<br />v = 8 m/s + 31.25 m/s² × 2 s<br />v = 8 m/s + 62.5 m/s<br />v = 70.5 m/s<br /><br />Therefore, the speed of the car after 2 seconds of acceleration is 70.5 m/s.