Kinematics and Newton's Laws: Exam Study Notes

One-Dimensional Kinematics

Relative Motion and Catching Up Problems

Relative motion problems involve analyzing the movement of two objects with respect to each other, often requiring the calculation of the time or distance needed for one object to catch up to another.

• Relative Velocity: The velocity of one object as observed from another moving object. If object A moves at velocity $v_A$ and object B at $v_B$ in the same direction, the velocity of A relative to B is $v_{A/B} = v_A - v_B$.

• Time to Catch Up: If a student starts at rest and a Frisbee moves away at constant velocity, the time to catch up is found by equating the distances traveled and solving for time.

• Equation: $d = v_{rel} \times t$ where $d$ is the initial separation, $v_{rel}$ is the relative velocity, and $t$ is the time to catch up.

• Example: If a Frisbee is thrown at $5.0\,\text{m/s}$ and a student starts $10.0\,\text{m}$ away, running at $4.0\,\text{m/s}$, the time to catch up is: $t = \frac{10.0}{5.0 - 4.0} = 10.0\,\text{s}$

One-Dimensional Kinematics

Position vs. Time Graphs

Position-time graphs visually represent the motion of objects. The slope of the graph at any point gives the object's velocity.

• Straight Line: Constant velocity (zero acceleration).

• Curved Line: Changing velocity (acceleration present).

• Steeper Slope: Higher speed.

• Example: If a student accelerates toward a Frisbee, the position-time graph will curve upward, indicating increasing velocity.

Graph Type	Physical Meaning
Straight, constant slope	Constant velocity
Curved, increasing slope	Acceleration (speeding up)
Curved, decreasing slope	Deceleration (slowing down)

Newton's Laws of Motion

Net Force and Acceleration

Newton's Second Law relates the net force acting on an object to its acceleration.

• Newton's Second Law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

• Equation: $F_{net} = m a$ where $F_{net}$ is the net force, $m$ is the mass, and $a$ is the acceleration.

• Direction: The acceleration is always in the same direction as the net force.

• Example: If a constant net force acts on an object, its acceleration remains constant and points in the direction of the force.