Question
A 2 kg rocket is subjected to a son tang of 400 N that accelerates it from rest to a speed of 100 m/s. How long did this event last?
Answers
GPT 3.5
To solve this problem, we will first use Newton's second law of motion to find the acceleration of the rocket.
Newton's second law states that the acceleration of an object is equal to the net force acting on it divided by its mass.
Given:
Mass of the rocket (m) = 2 kg
Net force acting on the rocket (F) = 400 N
Acceleration (a) = F/m = 400 N / 2 kg = 200 m/s^2
Next, we can use the kinematic equation to find the time it took for the rocket to reach a speed of 100 m/s.
The kinematic equation relates acceleration (a), initial velocity (u), final velocity (v), and time (t). The equation is:
v = u + at
Where:
u = initial velocity (0 m/s)
v = final velocity (100 m/s)
t = time
Rearranging the equation to solve for time, we have:
t = (v - u) / a
Substituting the given values, we get:
t = (100 m/s - 0 m/s) / 200 m/s^2
t = 0.5 s
Therefore, the event lasted for 0.5 seconds.
Newton's second law states that the acceleration of an object is equal to the net force acting on it divided by its mass.
Given:
Mass of the rocket (m) = 2 kg
Net force acting on the rocket (F) = 400 N
Acceleration (a) = F/m = 400 N / 2 kg = 200 m/s^2
Next, we can use the kinematic equation to find the time it took for the rocket to reach a speed of 100 m/s.
The kinematic equation relates acceleration (a), initial velocity (u), final velocity (v), and time (t). The equation is:
v = u + at
Where:
u = initial velocity (0 m/s)
v = final velocity (100 m/s)
t = time
Rearranging the equation to solve for time, we have:
t = (v - u) / a
Substituting the given values, we get:
t = (100 m/s - 0 m/s) / 200 m/s^2
t = 0.5 s
Therefore, the event lasted for 0.5 seconds.