When a car crashes into a wall, the car experiences a massive unbalanced force and decelerates rapidly. However, according to Newton's First Law, the passengers inside the car will continue moving forward at their initial velocity because no force has acted on them to stop them. Without seatbelts, their inertia would cause them to collide with the windshield or steering wheel. A seatbelt provides the necessary unbalanced force over a longer time duration (to reduce the impact force) to safely decelerate the passenger along with the car.

A common misconception is that a rocket accelerates by "pushing against the air." In the vacuum of space, there is no air. Rockets work entirely on Newton's Third Law. The rocket engine violently expels exhaust gases out of the back nozzle (Action). The equal and opposite reaction is the exhaust gases exerting a massive forward force on the rocket itself (Thrust). This is why a rocket can accelerate even in the emptiness of deep space.

A 10 kg block is placed on a smooth (frictionless) ramp inclined at $30^\circ$ to the horizontal. Calculate the acceleration of the block down the ramp. ($g = 9.8 \text{ m/s}^2$)

A 5 kg wooden crate is on a $25^\circ$ ramp. The coefficient of kinetic friction is $\mu_k = 0.2$. If it starts sliding from rest, what is its acceleration? ($g = 9.8 \text{ m/s}^2$)

A 20 kg block is on a $40^\circ$ incline with $\mu_k = 0.3$. A person pushes it up the incline with a horizontal force $P = 300 \text{ N}$. Find the block's acceleration up the ramp. ($g = 9.8 \text{ m/s}^2$)

A 1000 kg elevator is being pulled upward by a cable. If the tension in the cable is 12,000 N, what is the upward acceleration of the elevator? (Assume $g = 9.8 \text{ m/s}^2$)

Block A ($m_A = 4 \text{ kg}$) and Block B ($m_B = 6 \text{ kg}$) are connected by a massless string on a frictionless horizontal table. A horizontal force $F = 30 \text{ N}$ pulls on Block B. Find the acceleration of the system and the tension in the connecting string.

An Atwood machine consists of two masses, $m_1 = 3 \text{ kg}$ and $m_2 = 5 \text{ kg}$, connected by a massless string over a frictionless pulley. Find the acceleration of the masses and the tension in the string. ($g = 9.8 \text{ m/s}^2$)

A 50 kg box rests on a horizontal floor. A worker applies a horizontal pushing force of 200 N. The coefficient of kinetic friction between the box and the floor is $\mu_k = 0.3$. Determine the acceleration of the box. ($g = 9.8 \text{ m/s}^2$)

A 40 kg crate sits on a floor. The coefficient of static friction is $\mu_s = 0.6$ and kinetic friction is $\mu_k = 0.4$. A person pushes with $200 \text{ N}$ of horizontal force. Does the crate move? If not, what is the force of static friction?

A 25 kg lawnmower is pushed with a force of $150 \text{ N}$ directed at a downward angle of $30^\circ$ relative to the horizontal. If $\mu_k = 0.2$, what is its acceleration?