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An elaboration on how to use Newton's second law when dealing with multiple forces, forces in two dimensions, and diagonal forces.

This unit is about how things move along a straight line or, more scientifically, how things move in one dimension. Examples of this would be the movement (motion) of cars along a straight road or of trains along straight railway tracks.

In this lesson you will learn:

• to distinguish between distance and displacement
• to distinguish between speed and velocity
• understand acceleration
• interpret time-velocity graphs
• use equations of uniformly accelerated motion
• understand the concept of gravitational force

In this chapter, we’ll use vectors to expand our understanding of forces and motion into two dimensions. Most real-world physics problems (such as with the game of pool pictured here) are, after all, either two- or three-dimensional problems and physics is most useful when applied to real physical scenarios. We start by learning the practical skills of graphically adding and subtracting vectors (by using drawings) and analytically (with math). Once we’re able to work with two-dimensional vectors, we apply these skills to problems of projectile motion, inclined planes, and harmonic motion.

Newton's second law of motion is F = ma, or force is equal to mass times acceleration. Learn how to use the formula to calculate acceleration.

You want a projectile to fly as far as possible, at which angle should you launch it? We'll start with formulas for the initial velocity.

Plotting projectile displacement, acceleration, and velocity as a function of time.

Figuring out the horizontal displacement for a projectile launched at an angle.

• Determine how each parameter (initial height, initial angle, initial speed, mass, diameter, and altitude) affects the trajectory of an object, with and without air resistance.
• Predict how varying the initial conditions will affect a projectile’s path, and provide an explanation for the prediction.
• Estimate where an object will land, given its initial conditions.
• Determine that the x and y motion of a projectile are independent.
• Investigate the variables that affect the drag force.
• Describe the the effect that the drag force has on the velocity and acceleration.
• Discuss projectile motion using common vocabulary (such as: launch angle, initial speed, initial height, range, time).

Visualising position, velocity and acceleration in two-dimensions for projectile motion.