Question

What is the momentum (as a function of time) of a 5.0-kg particle moving with a velocity →v(t) = (2.0ˆi+4.0tˆj) m/s? What is the net force acting on this particle?

a) Momentum is (10ˆi+10ˆj) Ns; Net force is (4ˆi+8ˆj) N
b) Momentum is (8ˆi+8ˆj) Ns; Net force is (4ˆi+4ˆj) N
c) Momentum is (6ˆi+12ˆj) Ns; Net force is (2ˆi+4ˆj) N
d) Momentum is (4ˆi+16ˆj) Ns; Net force is (2ˆi+8ˆj) N

Answer 1

The momentum of a 5.0-kg particle moving with a given velocity is calculated and expressed as a function of time. The net force acting on the particle is found using Newton's second law of motion.

Step-by-step explanation:

The momentum of a particle can be calculated by multiplying its mass and velocity. In this case, the mass is 5.0 kg and the velocity is given as v(t) = (2.0î + 4.0tĵ) m/s. To find the momentum as a function of time, we can substitute the given velocity into the momentum equation and simplify.

The net force acting on the particle can be determined using Newton's second law of motion, which states that the net force is equal to the rate of change of momentum with respect to time. Since the momentum is a function of time, we can differentiate it with respect to time and then evaluate it at the given time.

Therefore, the momentum (as a function of time) is (10î + 20tĵ) Ns and the net force acting on the particle is (4î + 8ĵ) N.