What Forces Affect the Acceleration of an Airboat?

[hatcheezy]

An airboat with mass 4.38 102 kg, including passengers, has an engine that produces a net horizontal force of 8.08 102 N, after accounting for forces of resistance. a>how long does it take the airboat to reach a speed of 16.0 m/s? b>After reaching this speed, the pilot turns off the engine and drifts to a stop over a distance of 50.0 meters. Find the resistance force, assuming it's constant.

acceleration i found to be 1.84 m/s^2

a = 8.70 s
b = -1120 N

c> Suppose the pilot, starting again from rest, opens the throttle only partway. At a constant acceleration, the airboat then covers a distance of 64.0 meters in 11.5 seconds. Find the net force acting on the boat.

i need help finding c...i would appreciate steps in finding the solution-notjust the answer.

thanks in advance

 

[quantize]

use DeltaX = Vot + 1/2 at^2

remember he is starting from rest (Vo = 0, so the term drops)

solve for a(acceleration)

then multiply acceleration by the mass to get the net force from Newton's Second Law.

 

[nlightner]

a) To find the time it takes for the airboat to reach a speed of 16.0 m/s, we can use the equation v = u + at, where v is the final velocity, u is the initial velocity (which we assume to be 0), a is the acceleration, and t is the time. Rearranging the equation, we get t = (v-u)/a. Plugging in the values, we get t = (16.0 m/s - 0)/1.84 m/s^2 = 8.70 s. So it takes 8.70 seconds for the airboat to reach a speed of 16.0 m/s.

b) To find the resistance force, we can use the equation F = ma, where F is the force, m is the mass, and a is the acceleration. In this case, we know the mass (4.38x10^2 kg) and the acceleration (1.84 m/s^2). Plugging in the values, we get F = (4.38x10^2 kg)(1.84 m/s^2) = 807.12 N. However, this is the net force, so to find the resistance force, we need to subtract the engine force (808 N) from it. Therefore, the resistance force is 807.12 N - 808 N = -0.88 N. The negative sign indicates that the resistance force is acting in the opposite direction of motion.

c) To find the net force acting on the boat, we can use the same equation F = ma, but this time we know the acceleration (which is constant) and the distance traveled. We can use the equation v^2 = u^2 + 2as to find the final velocity, where u is the initial velocity (which is 0), a is the acceleration, s is the distance traveled, and v is the final velocity. Rearranging the equation, we get v = √(2as). Plugging in the values, we get v = √(2)(1.84 m/s^2)(64.0 m) = 16.9 m/s. Now, we can use the equation F = ma to find the net force. Plugging in the values, we get F = (4.38x10^2 kg)(1.84 m/s^2) = 807.