Final answer:
The speed of the hockey puck after being pushed by a force of 4.5 N over a distance of 3.0 m and starting at rest is 5.42 m/s, calculated using the work-energy principle.
Step-by-step explanation:
To determine the speed of the hockey puck after it has moved 3.0 m, we can use the work-energy principle. The work done by the force on the hockey puck is the product of the force and the distance moved in the direction of the force. Since the friction is ignored, the entire work done goes into the kinetic energy of the puck.
The work done (W) by the force (F) is given by:
W = F × distance = 4.5 N × 3.0 m = 13.5 joules
The initial kinetic energy
(KE_i) of the puck is 0 because it starts from rest. The final kinetic energy
(KE_f) is then equal to the work done:
KE_f = W
So,
KE_f = ½ × mass × (speed)^2
13.5 J = ½ × 0.165 kg × (speed)^2
Now we can solve for speed:
speed = √(2 × KE_f / mass) = √(2 × 13.5 J / 0.165 kg)
speed = 5.42 m/s