A force that changes with time, F=3t acts on a particle of mass 5 kg moving along the x-axis. The particle's velocity is 1 m/s along the negative x-axis at time t=0. Find the particle's velocity at the end of 6 s.
#impulse #momentum #collision
#impulse #momentum #collision
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00:00Hi friends, learning is the best investment for your future.
00:05Stay focused on your goals, make learning a daily habit, and never stop pursuing knowledge.
00:13In this series, we are asked to calculate the magnitude of the velocity of a particle
00:18after receiving a force.
00:20However, the magnitude of the force always changes as a function of time.
00:26How do we calculate the value of that velocity?
00:32Let's go to the discussion sheet.
00:35We don't know where the particle is located.
00:40Let's say the particle is initially at point zero.
00:45The particle's velocity is to the left.
00:51The particle then gets a force for a while to the right.
00:56Why do we know that the force is going to the right?
01:00Because the sign of the force is positive.
01:04Six seconds later, the particle reaches point one.
01:09It looks like the particle will change direction after receiving an impulse.
01:15Just write the impulse formula, J is equal to the integral of F with respect to time.
01:22Don't forget that the integration process requires a limit value.
01:26The lower limit is zero seconds.
01:29The upper limit is six seconds.
01:34From the problem sheet, the magnitude of the force is three T.
01:40Three is a fixed value.
01:42Fixed values can be excluded from the integral notation.
01:48I'm sure we have known the concept of integrals in high school.
01:52The integral of T with respect to time is half T squared.
01:59Enter the limits of integration.
02:02J is equal to 54 newtons per second.
02:07If you remember, impulse is a change in momentum.
02:13The final momentum is MV1, the initial momentum is MV0.
02:20The value of V0 is minus one meter per second, and the mass is five kilograms.
02:27Remember that the direction to the left has a negative sign.
02:31This is an easy calculation, V1 is about 9.8 meters per second.
02:38The sign of the velocity is positive.
02:41This means that the particle moves to the right after receiving a momentary impulse.
02:49Happy learning, everyone!