Download One-Dimensional Motion: Kinematics and Vectors and more Study notes Physics in PDF only on Docsity! 1 Chapter 2 Motion in One Dimension Kinematics Describes motion while ignoring the forces that caused the motion For now, will consider motion in one dimension Along a straight line Will use the particle model A particle is a point-like object, has mass but infinitesimal size Position Defined in terms of a frame of reference One dimensional, so generally the x- or y- axis The object’s position is its location with respect to the frame of reference Position-Time Graph The position-time graph shows the motion of the particle (car) The smooth curve is a guess as to what happened between the data points 2 Displacement Defined as the change in position during some time interval Represented as ∆x ∆x = x f - x i SI units are meters (m) ∆x can be positive or negative Different than distance – the length of a path followed by a particle Vectors and Scalars Vector quantities need both magnitude (size or numerical value) and direction to completely describe them Will use + and – signs to indicate vector directions Scalar quantities are completely described by magnitude only Average Velocity The average velocity is rate at which the displacement occurs The dimensions are length / time [L/T] The SI units are m/s Is also the slope of the line in the position – time graph f i average x xx v t t −∆ = = ∆ ∆ Average Speed Speed is a scalar quantity same units as velocity total distance / total time The average speed is not (necessarily) the magnitude of the average velocity 5 Instantaneous Acceleration The instantaneous acceleration is the limit of the average acceleration as ∆t approaches 0 2 2 0 lim x x x t v dv d x a t dt dt∆ → ∆ = = = ∆ Instantaneous Acceleration -- graph The slope of the velocity vs. time graph is the acceleration The green line represents the instantaneous acceleration The blue line is the average acceleration Acceleration and Velocity, 1 When an object’s velocity and acceleration are in the same direction, the object is? When an object’s velocity and acceleration are in the opposite direction, the object is? Acceleration and Velocity, 2 The car is moving with constant positive velocity (shown by red arrows maintaining the same size) Describe the acceleration 6 Acceleration and Velocity, 3 Velocity and acceleration are in the same direction Acceleration is uniform (blue arrows maintain the same length) Velocity is increasing (red arrows are getting longer) This shows positive acceleration and positive velocity Acceleration and Velocity, 4 Acceleration and velocity are in opposite directions Acceleration is uniform (blue arrows maintain the same length) Velocity is decreasing (red arrows are getting shorter) Positive velocity and negative acceleration
