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

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

Ch 2-3 Position and Displacement

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) t0 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

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) t0 = dv/dt=d2x/dt2

Velocity-time graph used to define object velocity at any time t and calculate its acceleration

a is slope of the line on velocity-time graph

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

Ch 2-7 Constant Acceleration

Equations for Motion with Constant Acceleration

v=v0+at x-x0=v0t+(at2)/2 v2=v0

2+2a(x-x0) x-x0=t(v+v0)/2 x-x0 =vt-(at2)/2

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

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

Ch 2-10 Graphical Integration in Motion Analysis