A motor pushes a boat through the water with the force of 2100 N; the water creates a resistance force of 1800 N.
What is the acceleration of 1200 kg boat?
(Do I use force equals mass times acceleration? 2100=1200a)
If it starts from rest how far will it move in 10 seconds?
(Do I take the acceleration and multiply it by 10?)
What will it's velocity be at the end of this time period?
I'm completely confused on this one
1. a = F/m = (2100-1800)/1200
2. d = (1/2) a t^2 = 50 a
3. v = a t = 10 a
NET force = 2100 - 1800 !!!!!!!
To find the acceleration of the boat, you can indeed use the equation Force = mass x acceleration (F = ma). In this case, the force the motor exerts on the boat is 2100 N (Newtons), and the resistance force of the water is 1800 N. The net force acting on the boat can be determined by subtracting the resistance force from the force exerted by the motor:
Net force = Force - Resistance force = 2100 N - 1800 N = 300 N.
Now, you can use Newton's second law of motion, F = ma, where F is the net force, m is the mass of the boat, and a is the acceleration. Rearranging the equation to solve for acceleration, you get:
a = F / m = 300 N / 1200 kg = 0.25 m/s^2.
Therefore, the acceleration of the 1200 kg boat is 0.25 m/s^2.
To determine how far the boat will move in 10 seconds, you need to use the equation of motion known as the kinematic equation:
distance = initial velocity x time + 0.5 x acceleration x time^2.
Since the boat starts from rest, the initial velocity is 0 m/s. Plugging in the values, you get:
distance = 0 x 10 + 0.5 x 0.25 x (10)^2 = 0 + 1.25 x 100 = 125 meters.
Therefore, the boat will move a distance of 125 meters in 10 seconds.
Finally, to find the velocity of the boat at the end of the 10-second time period, you can use the equation:
final velocity = initial velocity + acceleration x time.
Since the initial velocity was 0 m/s, you have:
final velocity = 0 + 0.25 x 10 = 2.5 m/s.
Therefore, the velocity of the boat at the end of the 10-second interval is 2.5 m/s.