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Chapter-2

Chapter-2. Motion Along a Straight Line. Ch 2-1 Motion Along a Straight Line. Motion of an object along a straight line Object is point mass Motion along a horizontal or vertical or inclined (line with finite slope) line Motion : Change in position No change in position, body at rest.

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Chapter-2

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  1. Chapter-2 Motion Along a Straight Line

  2. Ch 2-1 Motion Along a Straight Line • Motion of an object along a straight line • Object is point mass • Motion along a horizontal or vertical or inclined (line with finite slope) line • Motion: Change in position • No change in position, body at rest

  3. Ch 2-3 Position and Displacement • Axis are used to define position of an object • Position of an object defined with respect to origin of an axis • Position x of an object is its distance from the origin at any time t • Displacement x, a vector, is change in position. x = xf-xi • When an object changes its position, it has a velocity

  4. Ch 2-4 Average Velocity, Average Speed • Average Velocity vavg= x/ t vavg = (xf-xi) /(tf-ti) • Average speed Savg: a scalar Savg= total distance/ total time • Instantaneous Velocity v: v= lim (x/ t) t0 • Position-time graph used to define object position at any time t and to calculate its velocity • v is slope of the line on position-time graph

  5. Ch 2-6 Acceleration • When an object changes its velocity, it undergoes an acceleration • Average acceleration aavg aavg = v/ t = (vf-vi) /(tf-ti) • Instantaneous acceleration a: a= lim (v/ t) t0 = dv/dt=d2x/dt2 • Velocity-time graph used to define object velocity at any time t and calculate its acceleration • ais slope of the line on velocity-time graph

  6. Ch 2-7 Constant Acceleration • Constant Acceleration: • Variable Slope of position-time graph • Constant Slope of velocity -time graph • Zero Slope of acceleration -time graph • For constant acceleration a =aavg= (vf-vi)/(tf-ti) vavg= (vf+vi)/2

  7. Equations for Motion with Constant Acceleration • v=v0+at • x-x0=v0t+(at2)/2 • v2=v02+2a(x-x0) • x-x0=t(v+v0)/2 • x-x0 =vt-(at2)/2

  8. Ch 2-9 Free Fall Acceleration • Free fall acceleration ‘g’ due to gravity • Directed downward towards Earth’s center along negative y-axis • with a = -g = -9.8 m/s2 • equations of motion with constant acceleration are valid for free fall motion

  9. Ch 2-10 Graphical Integration in Motion Analysis • x-x0=vt x-x0= v dt v dt= area between velocity curve and time axis from t0 to t • Similarly v-v0= a dt a dt = area between acceleration curve and time axis from t0 to t

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