a 10kg toy mootorized boat uses 2.0 W of power, has a constant accel from rest and reaches a certain speed in 10 s on a horizontal surface. what was the final speed ?
To find the final speed of a 10kg motorized boat that uses 2.0 W of power and undergoes constant acceleration from rest, we can use the formula:
Power (P) = Force (F) x Velocity (V)
Since we are given the power, we need to determine the force acting on the boat. We can use Newton's second law of motion, which states:
Force (F) = Mass (m) x Acceleration (a)
In this case, the mass is given as 10 kg and the boat starts from rest, so the initial velocity (u) is 0 m/s. We are also given the time taken for the boat to reach the final speed, which is 10 seconds.
First, let's find the acceleration of the boat using the formula:
Acceleration (a) = (Final Velocity (v) - Initial Velocity (u)) / Time (t)
Since the boat starts from rest, the final velocity is equal to the final speed. Plugging in the values, we have:
a = (v - 0) / 10
Next, we can substitute the value of acceleration into the force equation:
F = m x a
F = 10 kg x a
Now, let's substitute the force value into the power equation:
P = F x v
2.0 W = (10 kg x a) x v
We can rearrange this equation to solve for the final velocity:
v = 2.0 W / (10 kg x a)
Substituting the value for acceleration obtained earlier:
v = 2.0 W / (10 kg x ((v - 0) / 10))
v = 2.0 W / (10 kg x v / 10)
Now we can cross-multiply to solve for v:
v x 10 kg x v = 2.0 W x 10
10 kg x v^2 = 20 W
v^2 = 20 W / 10 kg
v^2 = 2 m^2/s^2
Taking the square root of both sides, we can find the final velocity (v):
v = √2 m/s
Therefore, the final speed of the toy motorized boat is approximately 1.41 m/s.