A force of 10N acts on a 5 kg mass for a short 0.5 s duration. What is the resulting velocity of the mass if it started with no velocity?

Question

anonymous · Answer

Lets us consider Newton's Second Law, which mathematically boils down to $$F = m*a$$
Where F is the force being applied to an object, m is the mass of the object and a is the acceleration of the object. The force (50 N) is being applied to a 5 kg object, so the resulting acceleration is:
$$a = F/m = 10 m/s^2$$
Should you integrate this with respect to time, you will find the velocity, due the the fact that acceleration is the derivative of velocity. So, using a simple integration, we find that:$$v = a*t +c$$
Where a is the acceleration, t is the time, and c is a constant. Using the initial conditions, we find that v = 0 at t = 0. Using these values in the equation above gives c = 0. Therefore, the final velocity is:
$$v = a*t = 10 m/s^2 * 0.5 s = 5 m/s$$

anonymous · Answer

Newton's Second Law is usually represented as, $$F=m*a$$ but force can also be interpreted a change in momentum, mass*velocity.$$F = d(m*v)/dt$$ By bringing the dt to the left hand side of the equation and integrating, one finds the new equation, $$F*t=m(v-v _{0})$$ The quantity F*t is called impulse. The equation for impulse is more commonly written as $$I=m \Delta v$$ Plugging in the values given
$$10N*.5s=5kg(v-0)$$
Therefor the final velocity is:
$$v=1m/s$$