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• Speed is defined as the distance traveled per unit of time, regardless of direction. It is a scalar quantity and is typically expressed in units such as meters per second (m/s).

• Velocity is defined as the displacement (the shortest distance from the initial to the final position) per unit of time. Unlike speed, velocity is a vector quantity, meaning it has both magnitude and direction. It's also expressed in units such as meters per second (m/s).

• Acceleration is defined as the rate of change of velocity per unit of time. It is also a vector quantity, indicating both magnitude and direction. Acceleration is typically expressed in units such as meters per second squared (m/s²).

Relationships Between d-t, v-t, and a-t Graphs in the IB Curriculum

1. Distance-Time (d-t) Graphs:

   • Represents the distance traveled by an object over time.

   • The slope of the graph corresponds to the speed of the object.

   • A uniform slope indicates constant speed, while a changing slope indicates acceleration or deceleration.

2. Velocity-Time (v-t) Graphs:

   • Displays how velocity changes with respect to time.

   • The slope of the v-t graph represents acceleration.

   • A positive slope indicates an increase in velocity (acceleration), while a negative slope indicates a decrease (deceleration).

   • The area under the curve gives the displacement of the object over a time interval.

3. Acceleration-Time (a-t) Graphs:

   • Shows the variation of acceleration over time.

   • The values on the graph indicate the magnitude and direction of acceleration (positive or negative).

   • The area under the a-t graph represents the change in velocity during that time period.

Key Concepts:

• The relationship between these graphs is crucial in understanding motion.

• By analyzing d-t, v-t, and a-t graphs together, one can derive critical information about speed, velocity, displacement, and acceleration, which are all foundational concepts in IB Physics.

In the context of the SUVAT equations in the IB curriculum, each variable represents the following:

1. S (Displacement): The distance traveled by an object in a specific direction. It is a vector quantity and is typically measured in meters (m).

2. U (Initial Velocity): The velocity of the object at the starting point of observation. This is the velocity before any acceleration takes place, measured in meters per second (m/s).

3. V (Final Velocity): The velocity of the object at the end of the time interval in consideration. This is the velocity after any acceleration has occurred, also measured in meters per second (m/s).

4. A (Acceleration): The rate of change of velocity per unit of time. This is a vector quantity and can be positive (acceleration) or negative (deceleration), measured in meters per second squared (m/s²).

5. T (Time): The duration over which the motion occurs, measured in seconds (s).

Here are some questions related to SUVAT with answers according to the IB curriculum:

Question 1

A car accelerates uniformly from rest to a velocity of 20 m/s over a time of 5 seconds. What is the acceleration of the car?

Answer

Using the equation: A = (V - U) / TA = (20 m/s - 0 m/s) / 5 s = 4 m/s².

Question 2

An object is thrown vertically upward with an initial velocity of 15 m/s. What will be its displacement after 3 seconds? (Assuming acceleration due to gravity is -9.81 m/s²)

Answer

Using the equation S = Ut + 0.5At²:S = (15 m/s)(3 s) + 0.5(-9.81 m/s²)(3 s)²S = 45 m - 44.145 m = 0.855 m.

Question 3

A projectile is launched at an angle with an initial velocity of 30 m/s. If it reaches a maximum height where the final vertical velocity is 0 m/s, what is the maximum height reached? (Use g = 9.81 m/s²)

Answer

Using the equation V² = U² + 2AS:0 = (30 m/s)² + 2(-9.81 m/s²)SS = (30 m/s)² / (2 * 9.81 m/s²) = 45.9 m.

Question 4

A cyclist moves at an initial speed of 10 m/s and accelerates at 2 m/s². How far will the cyclist travel in 8 seconds?

Answer

Using the equation S = Ut + 0.5At²:S = (10 m/s)(8 s) + 0.5(2 m/s²)(8 s)²S = 80 m + 0.5(2)(64) = 80 m + 64 m = 144 m.

Question 5

A ball is dropped from a height of 45 m. How long does it take to reach the ground? (Use g = 9.81 m/s²)

Answer

Using the equation S = Ut + 0.5At² with U = 0 m/s:45 m = 0 + 0.5(9.81 m/s²)(t²)=> t² = (2 * 45 m) / (9.81 m/s²)=> t ≈ 3.03 seconds.

Freefall is defined as the motion of an object under the influence of gravitational force alone, without any resistance from air or other forces. In IB Physics, freefall is characterized by a constant acceleration, equal to the acceleration due to gravity (g), which is approximately 9.81 m/s² near the surface of the Earth. During freefall, an object's velocity increases by approximately 9.81 m/s for each second it falls, and its displacement can be calculated using the SUVAT equations assuming initial velocity (U) is zero when dropped.

A projectile is any object that moves near the Earth’s surface and is acted upon only by gravity. (We neglect air resistance.)

Defining characteristics:

1. constant vertical acceleration

2. constant horizontal velocity

Projectile motion is defined as the motion of an object that is projected into the air and is subject only to the influence of gravity (neglecting air resistance). In IB Physics, projectile motion is characterized by two components: horizontal and vertical motion.

1. Constant Horizontal Velocity: The horizontal component of motion is uniform, meaning the object moves at a constant speed in the horizontal direction since there are no horizontal forces acting on it (ignoring air resistance).

2. Vertical Acceleration: The vertical component of motion is influenced by gravity, resulting in a constant downward acceleration of approximately 9.81 m/s². The object’s vertical velocity changes over time due to this acceleration.

Projectile motion is often analyzed using the kinematic equations (SUVAT equations) to determine parameters such as range, maximum height, and time of flight, factoring in both the horizontal and vertical components separately.

Additional Vocabulary:

Time of flight: the amount of time it takes for a projectile to complete its motion

Range: The horizontal distance travelled by a projectile

In an idealized situation without air resistance, all objects in free fall near the Earth's surface would experience the same acceleration due to gravity, denoted as ggg (approximately 9.81 m/s²). This follows from Newton's Second Law of Motion (F=maF = maF=ma) and the fact that the force acting on an object in free fall is solely its weight (F=mgF = mgF=mg). When substituted, the mass cancels out, leading to a uniform acceleration of ggg, independent of the object's mass.

However, in real-world conditions, falling objects do not always accelerate at the same rate due to the presence of air resistance (drag force). According to Newton’s Second Law, the net force on a falling object is given by:

The drag force depends on factors such as:

• The velocity of the object (higher velocity increases drag).

• The cross-sectional area (larger area increases drag).

• The shape and texture of the object (which affect air resistance).

• The density of air (affecting how much resistance is experienced).

As an object falls, its velocity increases, leading to a greater drag force. Eventually, the object reaches terminal velocity, where the drag force equals the gravitational force (mg=Fdragmg​), resulting in zero net force and thus zero acceleration (constant velocity).

This explains why a feather and a stone, for example, do not fall at the same rate in normal conditions. The feather, having a larger surface area relative to its mass, experiences a greater proportion of drag force and reaches terminal velocity quickly. In contrast, the stone, with a higher density and smaller cross-sectional area, continues accelerating for longer before reaching its terminal velocity.

In the IB framework, this is analyzed under Newton’s Laws, the concept of forces and motion, and the effects of fluid resistance on acceleration.

• Air resistance (the frictional force exerted on a falling object by the air it passes through)

• Also called drag

• Depends on the shape and speed of an object

  • Larger area -> more drag

  • Faster -> more drag

• This happens in other fluids as well, not just air

Terminal Velocity

• When a falling object reaches a certain velocity, the gravitational force is matched by the drag

• At this point, the falling object stops accelerating, falls at a constant velocity

This constant velocity is called the terminal velocity