Quick questions on Linear motion and Newton's laws: QCE Physics Unit 2 Year 11

A body at rest stays at rest, and a body in motion stays in motion at constant velocity, unless acted on by a net external force. Inertia is the resistance of mass to a change in motion, so a more massive object is harder to accelerate or stop. Seatbelts and headrests are direct applications: when a car stops suddenly, the passenger continues forward at the original velocity until a force restrains them.

The net force on a body equals the rate of change of its momentum; for constant mass this reduces to $F_{\text{net}} = ma$. The acceleration is in the direction of the net force, is proportional to the net force, and is inversely proportional to mass. This is the central problem-solving equation: resolve all forces, find the net force, then divide by mass.

When body A exerts a force on body B, body B exerts an equal and opposite force on body A. The two forces are equal in magnitude, opposite in direction, of the same type, and crucially act on different bodies, so they never cancel each other. A swimmer pushes water backward and the water pushes the swimmer forward.

Choose one positive direction and keep it for the whole problem. If up is positive, then $g = -9.8\ \text{m s}^{-2}$ and an upward initial velocity is positive.

State Newton's three laws of motion. [3 marks]

A $1200 \text{ kg}$ car accelerates from $10 \text{ m s}^{-1}$ to $25 \text{ m s}^{-1}$ in $5.0 \text{ s}$. Calculate the acceleration, the net force and the impulse. [4 marks]

A $400 \text{ kg}$ Bremer bridge gondola accelerates upward at $0.5 \text{ m s}^{-2}$ for $4.0 \text{ s}$ from rest. (a) Calculate the rope tension and the displacement. (b) Determine the kinetic energy and check via work-energy theorem.