Kinematic Graphs for Projectile Motion

When analyzing projectile motion, we separate the motion into horizontal and vertical components.

This separation reveals simple, predictable patterns in the kinematic graphs that help us understand the motion completely.

The Fundamental Principle

In projectile motion (neglecting air resistance), the horizontal and vertical motions are independent:

• Horizontally: We have that $a_x = 0$. This means $v_x$ remains constant, and position $x(t)$ increases linearly.
• Vertically: Gravity provides constant downward acceleration $a_y = -g$, causing $v_y$ to decrease linearly and the position $y(t)$ to form a parabola.

Remember: The slope of a position graph gives velocity, and the slope of a velocity graph gives acceleration.

Horizontal Motion Analysis

Let's examine the horizontal motion in isolation. Since no horizontal forces act on the projectile:

Observe how the horizontal velocity component $v_x$ remains constant throughout the entire trajectory. Press Play to see this in action.

Now examine the corresponding kinematics graphs:

The horizontal graphs show:

• Acceleration: Zero throughout (no horizontal force)
• Velocity: Constant (horizontal line)
• Position: Linear increase (straight line with constant slope)

Vertical Motion Analysis

Now let's focus on the vertical motion, where gravity acts continuously:

Press Play and observe how $v_y$ decreases from positive (upward) through zero at the apex. Press play again to then see it go negative (downward). Gravity continuously pulls downward at $g = 9.8$ m/s².

The corresponding vertical motion graphs: