Physics Lesson 4 Linear Motion Eleanor Roosevelt High School Chin-Sung Lin

Relative Motion

Motion is Relative  All motion is relative  Motion is meaningless unless we specify motion relative to a specific object  Each such choice is known as a frame of reference

Relative Motion Frame of Reference  An arbitrary coordinate system with reference to which the position or motion of something is described or physical laws are formulated

Relative Motion Frame of Reference  Two frames of reference moving relative to each other with a constant velocity are completely equivalent, and the same laws of mechanics hold in both

Distance & Displacement

Distance A distance (d) is a scalar quantity A distance is a numerical description of how far apart objects are or the initial to the final position of an object Unit: meter (m) Distance

Displacement A displacement (d) is a vector quantity A displacement represents the length and direction of the shortest distance from the initial to the final position of an object Its direction is from the initial location to the final location Unit: meter (m) Displacement

Speed & Velocity

Speed A speed (v) is a scalar quantity Distance (d) covered per unit of time (t). Speed is a measure of how fast something is moving. It is the rate at which distance is covered Unit: meters per second (m/s), miles per hour (mi/h), kilometers per hour (km/h)

Average Speed Average speed (v): v = d / t d = total distance covered (m) t = time interval (s) t d slope = v

Instantaneous Speed The speed (v) at any instance of an object is called the instantaneous speed It is equal to the slope of the tangent line at that moment t d slope = v

Constant Speed The speed at any instance of an object is constant t d slope = v x t v slope = 0 vxvx

Constant Speed The speed at any instance of an object is constant t d slope = v x t v slope = 0 vxvx

Constant Speed The speed at any instance of an object is constant t d slope = 0 t v 0

Velocity A velocity (v) is a vector quantity Velocity is the measurement of the rate and direction of change in the displacement (d) of an object v = d / t The speed is the magnitude of velocity Unit: meters per second (m/s), miles per hour (mi/h), kilometers per hour (km/h)

Speed & Velocity Speed has only magnitude Velocity has magnitude and direction

Average Velocity Average velocity (v): v = d / t d = total displacement (m) t = time interval (s) t d slope = v

Instantaneous Velocity The velocity (v) at any instance of an object is called the instantaneous velocity It is equal to the slope of the tangent line at that moment t d slope = v

Constant Velocity To have a constant velocity requires both constant speed and constant direction Motion at constant velocity is motion in a straight line at constant speed t d slope = v x t v slope = 0 vxvx

Constant Velocity The velocity at any instance of an object is constant t d slope = v x t v slope = 0 vxvx

Constant Velocity The velocity at any instance of an object is constant t d slope = 0 t v 0

Constant Velocity The velocity at any instance of an object is constant t d slope = v x t v slope = 0 vxvx

Constant Velocity The velocity at any instance of an object is constant t d slope = v x t v slope = 0 vxvx

Change Velocity Either speed or direction (or both) is changing and then the velocity is changing

Change Velocity Motion at constant speed can have changing velocity all the time when it moves along a curved path Constant speed Changing velocity

Change Velocity Car example: In a car there are three controls that are used to change the velocity: the gas pedal, the brake and the steering wheel

Acceleration

An acceleration (a) is a vector quantity acceleration is the rate of change of velocity with time a = Δv / t a = acceleration (m/s 2 )  v = change of velocity (m/s) t = time interval (s)

Acceleration Acceleration: the slope of the velocity-time (v-t) graph t v slope = a x (acceleration)

Constant Acceleration The acceleration at any instance of an object is constant In high school physics, we only deal with constant acceleration t v slope = a x t a slope = 0 axax

Displacement, Velocity & Acceleration d-t t v slope = a x t a slope = 0 axax t d slope = increasing at constant rate v-t a-t

Displacement, Velocity & Acceleration d-t t v slope = a x t a slope = 0 axax t d slope = decreasing at constant rate v-t a-t

Change Acceleration Either speed or direction (or both) is changing, i.e., changes in the state of motion, and then the acceleration is changing The acceleration applies to increases as well as decreases in speed The decrease in speed is also called deceleration, or negative acceleration

Acceleration An acceleration (a) is also a scalar quantity When linear (straight-line) motion is considered, it is common to use speed and velocity interchangeably and the acceleration may be expressed as the rate at which speed changes a = Δv / t a = acceleration (m/s 2 )  v = change of speed (m/s) t = time interval (s)

Acceleration Car example: Cars having good acceleration means being able to change velocity quickly and does not necessarily refer to how fast something is moving

Free Fall

When there is no air resistance and the gravity is the only thing affecting a falling object

Elapsed Time The elapsed time is the time that has elapsed, or passed, since the beginning of the fall

Acceleration due to Gravity Acceleration due to gravity (g): The free falling object is experiencing acceleration, i.e., a change in speed The value of acceleration (g) is about 10 m/s 2. More accurately, g is 9.81 m/s 2 The speed increase 9.81 m/s per second g is 9.81 m/s 2

Acceleration due to Gravity 0 s 1 s 5 s 2 s 4 s 3 s 6 s 7 s v = 30 m/s v = 20 m/s v = 10 m/s v = 0 m/s v = -40 m/s v = -30 m/s v = -20 m/s v = -10 m/s v = 0 m/s

Acceleration due to Gravity t a Constant Acceleration g a-t g = m/s 2

Velocity Change due to Gravity t v slope = g v-t v = 0 g = m/s 2

Displacement Change due to Gravity d-t t d slope decreasing at constant rate dydy v = 0 g = m/s 2 d = d y d = 0

Displacement, Velocity & Acceleration due to Gravity d-t t v slope = g t a slope = 0 g t d slope decreasing at constant rate v-t a-t dydy

Displacement, Velocity & Acceleration due to Gravity d-t t v slope = g t a slope = 0 g t d slope decreasing at constant rate v-t a-t dydy Constant Direct Proportion Quadratic Parabola

Displacement, Velocity & Acceleration due to Gravity d-t t v slope = g t a slope = 0 g t d slope increasing at constant rate v-t a-t dydy Slope of v-t Area under v-t

Instantaneous Velocity in Free Falling t v slope = g v-t t = t f v = v f v f = ?

Instantaneous Velocity in Free Falling t v slope = g v-t t = t f v = v f v f = ? v = gt v f = gt f

Instantaneous Velocity in Free Falling t v slope = g v-t t = t f v = v f The instantaneous velocity of an object falling from rest: instantaneous velocity = acceleration x elapsed time v = gt

Instantaneous Velocity in Free Falling t v slope = g v-t t = t f v = v f When the falling object has initial velocity (v i ), whether the object is moving upward or downward, the acceleration due to gravity is always the same (–9.81 m/s 2 ) the entire time The final velocity (v f ), the instantaneous velocity, is: v f = v i + gt v = v i

Instantaneous Velocity in Free Falling t v slope = g v-t t = t f v = v f When the falling object has initial velocity (v i ), whether the object is moving upward or downward, the acceleration due to gravity is always the same (–9.81 m/s 2 ) the entire time The final velocity (v f ), the instantaneous velocity, is: v f = v i + gt g = (v f - v i ) / t v = v i

Instantaneous Velocity in Free Falling t v slope = g v-t t = t f v = v f When the falling object has initial velocity (v i ), whether the object is moving upward or downward, the acceleration due to gravity is always the same (–9.81 m/s 2 ) the entire time The final velocity (v f ), the instantaneous velocity, is: v f = v i + gt g = (v f - v i ) / t g = Δv / t v = v i

Average velocity in Free Falling t v slope = g v-t tftf vfvf For any object moving in linear motion with constant acceleration, the average velocity (v) is: average velocity = (initial velocity + final velocity) / 2 0 vivi v v = v i + v f 2

Displacement-Time Formula Given initial velocity (v i ) and time (t), and based on the formulas we have gotten, find the displacement-time formula v = v i + v f 2 v f = v i + gt v = d / t

Displacement-Time Formula Given initial velocity (v i ) and time (t), and based on the formulas we have gotten, find the displacement-time formula v = v i + v f 2 v f = v i + gt v = d / t d = v i t + ½ gt 2

Displacement Change due to Gravity d-t t d Parabola dydy v = 0 g = m/s 2 d = d y d = 0 d = d y + v i t + ½ gt 2

Distance Change due to Gravity d-t t d Parabola v = 0 g = 9.81 m/s 2 d = 0 d = d y d = v i t + ½ gt 2

Displacement-Velocity Formula Given initial velocity (v i ) and displacement (d), and based on the formulas we have gotten, find the displacement- velocity formula d = v i t + ½ gt 2 g = (v f - v i ) / t

Displacement-Velocity Formula Given initial velocity (v i ) and displacement (d), and based on the formulas we have gotten, find the displacement- velocity formula d = v i t + ½ gt 2 g = (v f - v i ) / t v f 2 = v i 2 + 2gd

Summary of Free Falling Formulas v = v i + v f 2 v f = v i + gt v = dt d = v i t + ½ gt 2 g = Δv / t v f 2 = v i 2 + 2gd

Summary of Linear Motion Formulas v = v i + v f 2 v f = v i + at v = dt d = v i t + ½ at 2 a = Δv / t v f 2 = v i 2 + 2ad

The End