Force and Motion Test. 1

Work done against gravity is equal to the gain in potential energy: W = PE = mgh = 5 kg * 9.8 m/s² * 2 m = 98 J.

The range formula R = (v_i² sin(2θ))/g is maximized when sin(2θ) = 1, which occurs when 2θ = 90°, so θ = 45°.

Newton's third law states that for every action, there is an equal and opposite reaction. These forces act on different bodies.

The resultant displacement is found using the 3D Pythagorean theorem: d = √(x² + y² + z²) = √(8² + 6² + 10²) = √(64 + 36 + 100) = √200 = 10√2 m.

First, find acceleration: a = Δv/t = 20/10 = 2 m/s². Then use s = v_i*t + ½at² = 0*10 + ½(2)(10)² = 100 m.

Newton's first law, the law of inertia, states that an object's state of motion will not change unless acted upon by a net external force.

By conservation of momentum, m_gun * v_gun + m_bullet * v_bullet = 0. So, v_gun = -(m_bullet * v_bullet) / m_gun = -(0.02 kg * 150 m/s) / 10 kg = -0.3 m/s.

Work is calculated as W = Fd cosθ. Since cos(90°) = 0, the work done is zero when the force is perpendicular to the displacement.

By conservation of energy, initial PE = final KE. So, mgh = ½mv². Solving for v gives v = √(2gh).

The horizontal component of velocity (v_x = v cosθ) remains constant throughout projectile motion. So, v_x = 10 * cos(60°) = 10 * 0.5 = 5 m/s.

In uniform circular motion, the direction of velocity is constantly changing, but its magnitude (speed) remains constant.

Velocity is the rate of change of displacement (v = Δd/Δt), which corresponds to the slope of the displacement-time graph.

According to Newton's second law, F = ma. Therefore, acceleration a = F/m = 10 N / 2 kg = 5 m/s².

Since velocity is displacement per unit time, the product of velocity and time (the area under the graph) gives the total displacement.

The defining characteristic of a perfectly elastic collision is the conservation of both total momentum and total kinetic energy of the system.

Power is defined as the work done per unit of time (P = W/t), measured in Watts (Joules/second).

The impulse-momentum theorem states that the impulse (FΔt) applied to an object is equal to the change in its momentum (Δp).

Impulse is Force × time, so its unit is the Newton-second (N s). It is equivalent to the unit of momentum, kg m/s.

The standard formula for kinetic energy, the energy of motion, is KE = ½mv².

Momentum (p = mv) has both magnitude and direction, making it a vector quantity. Speed, distance, and mass are scalars.