Using ω = ω₀ + αt, we set ω = 0, thus 0 = 12 rad/s - 3 rad/s² * t, giving t = 4 s.

Horizontal component = F cos(θ) = 30 N × cos(60°) = 30 N × 0.5 = 15 N.

Power = Work / Time = 200 J / 10 s = 20 W.

Power = Work / Time = 200 J / 5 s = 40 W.

The person's speed relative to a stationary observer is the sum of their speeds: 10 m/s + 2 m/s = 12 m/s.

The person's speed relative to the ground is the speed of the train plus the speed of the person: 60 km/h + 4 km/h = 64 km/h.

The plane's speed relative to the ground is 250 km/h - 50 km/h = 200 km/h.

Angular momentum L = Iω = 2 kg·m² × 10 rad/s = 20 kg·m²/s.

Using the formula d = 0.5 * a * t², first find a = (v_f - v_i) / t = (10 - 0) / 5 = 2 m/s². Then, d = 0.5 * 2 * (5)² = 25 m.

Average speed = total distance / total time = 400 m / 50 s = 8 m/s.

The solid disk has a lower moment of inertia than the hollow cylinder, allowing it to accelerate faster down the incline.

As the source moves away, the frequency decreases, so the observer hears a frequency less than 400 Hz.

Using the formula t = √(2h/g), where h = 20 m and g = 9.8 m/s², we get t = √(2 * 20 / 9.8) ≈ 2.02 s.

Time to reach the highest point is given by t = v/g, where v = 30 m/s and g = 9.8 m/s², so t = 30 / 9.8 ≈ 3.06 s.

The swimmer's speed relative to the bank when swimming upstream is the swimmer's speed minus the current: 3 km/h - 2 km/h = 1 km/h.

Using τ = Iα, we have α = τ/I = 10 N·m / 2 kg·m² = 5 rad/s².

The passenger's speed relative to the ground is the speed of the train plus the speed of the passenger: 90 km/h + 5 km/h = 95 km/h.

Using the formula a = (v_f - v_i) / t, where v_f = 0 m/s, v_i = 80 m/s, and t = 10 s, we get a = (0 - 80) / 10 = -8 m/s².

First convert speed to m/s: 72 km/h = 20 m/s. Deceleration = (final velocity - initial velocity) / time = (0 - 20) / 5 = -4 m/s².

Average velocity = total distance / total time = 150 m / 10 s = 15 m/s.

Angular momentum L = Iω = 2 kg·m² × 10 rad/s = 20 kg·m²/s.

Angular momentum L = Iω = 2 kg·m² * 4 rad/s = 8 kg·m²/s.

Force F = k * |q₁ * q₂| / r² = (8.99 x 10^9 N m²/C² * |3 x 10^-6 C * -2 x 10^-6 C|) / (0.1 m)² = 0.54 N.

Faraday's law states that the induced emf is proportional to the rate of change of magnetic flux through the loop.

Kirchhoff's Voltage Law states that the sum of the voltages around a closed loop is equal to zero.

Using F = ma, acceleration a = F/m = 10 N / 2 kg = 5 m/s².

Newton's second law states that force is equal to mass times acceleration (F = ma).

According to Newton's third law, for every action, there is an equal and opposite reaction. Therefore, the wall exerts a force of 30 N back on you.

Newton's third law states that for every action, there is an equal and opposite reaction.

Newton's third law states that for every action, there is an equal and opposite reaction.