a net force of 2.50*10^3 n on a rocket of mass 1.70*10^3kg how long does it take this force to increase the rockets velocity from 0 m/s to 2.15*10^2 m/s
To calculate the time it takes for the force to increase the rocket's velocity, we can use Newton's second law of motion and the equation for velocity.
Newton's second law states that the net force acting on an object is equal to the product of the object's mass and its acceleration: F = m * a.
In this case, we have a net force of 2.50 * 10^3 N and a rocket mass of 1.70 * 10^3 kg. So, the acceleration can be calculated as follows:
a = F / m = (2.50 * 10^3 N) / (1.70 * 10^3 kg)
Now, we need to find the time it takes for the rocket's velocity to increase from 0 m/s to 2.15 * 10^2 m/s. We can use the equation for velocity:
v = u + at
Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
In this case, the initial velocity (u) is 0 m/s, the final velocity (v) is 2.15 * 10^2 m/s, and we have already calculated the acceleration (a).
We can rearrange the equation to solve for time (t):
t = (v - u) / a
Now, substituting the given values:
t = (2.15 * 10^2 m/s - 0 m/s) / [(2.50 * 10^3 N) / (1.70 * 10^3 kg)]
Simplifying further:
t = (2.15 * 10^2 m/s) * [(1.70 * 10^3 kg) / (2.50 * 10^3 N)]
Multiplying the values:
t = (2.15 * 10^2 m/s) * (1.70 * 10^3 kg / 2.50 * 10^3 N)
Now, multiplying the numerator and denominator:
t = (2.15 * 1.70 * 10^2 * 10^3) / (2.50 * 10^3)
t = (3.655 * 10^5) / (2.50 * 10^3)
t ≈ 146.2 seconds
Therefore, it takes approximately 146.2 seconds for the given force to increase the rocket's velocity from 0 m/s to 2.15 * 10^2 m/s.