PS112: Physics
By Somchai
Thangsathityangkul Lecture 4:
One dimension motion
(Continue)
Constant velocity motion

An object move with an uniform motion
slope of x(t) = constant
v = v(t) = v 0 , x = x 0 at t= 0
at an y tim e t p o sitio n is at x (t)
 v = v0 =
x (t) - x 0
t-0
 x (t) = x 0 + v 0 t
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Acceleration
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EXAMPLE
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Constant Acceleration

For constant a(t) = a =
v (t )  v0
t0
, v  v 0 at t = 0
 v ( t )  v 0  at
if object is at x0 at time t0
after an elapsed tim t it
will be at x  x 0  vt
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Constant Acceleration
Since v(t) increases uniformly with t
v 
v0  v (t )

x (t )  x0
2
 x (t )  x0 

t
1( v 0  v ( t )) t
( v0  v0  a t )t
2
2
 (v0 
 x (t )  x0  v0t 
1
at
1
a t )t
2
2
2
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Constant Acceleration
v (t )  v0  a t
We have
So,
t
Then ,
v  v0
a
,  x (t )  x0  v0 (
v  v0
)
a
1
2
a(
v  v0
)
2
a
v  v  2 a ( x  x0 )
2
2
0
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Constant Acceleration
Using calculus :
x (t )  x0  v0t 
v (t ) 
dx
dt
a (t ) 
dv
1
at
2
2
 v0  a t
 a ( a is a co n stan t )
dt
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Example

How long does it take a car to travel 30 m if it
accelerates from rest at a rate of 2.0 m/s2 ?
Solution: Known x0 = 0, v0 = 0 , a = 2.0 m/s2,
x=30 m  t = ?
from eq :
x (t )  x0  v0t 
1
at
2
2
3 0 m = 0 + (0 )t +
1
 2t
2
2
 t =
3 0  5 .5 s
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Example

Particle is at the coordinate position x0=5m
at t=0 and moving with a velocity v0=20 m/s.
The particle then starts to decelerate. At
t=10 s the particle has a velocity v=2 m/s
a) What is the acceleration ?
b) What is the position function ?
c) How long is it before the particle returns
to x=5m.
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EXAMPLE
A car traveling at a constant speed of 45.0 m/s passes a trooper hidden
behind a billboard. One second after the speeding car passes the
billboard, the trooper sets out from the billboard to catch it,
accelerating at a constant rate of 3.00 m/s2. How long does it take
her to overtake the car?
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Try this
An alpha particle travels along the inside of
a straight hollow tube 2.0 m long which
forms part of a particle accelerator.
a) If one assumes uniform acceleration,
what is the acceleration of the particle, if it
enters at a speed of 1.0x104 m/s and
leaves at 5.0x106 m/s ?
b) How long is it in the tube ?
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Try this

You break your car from a velocity of 85
km/hr to 45 km/hr over a distance of 105 m.
a) What is the acceleration ?
b) How much time elapses during this
interval ?
c) If you were to continue braking with the
same acceleration, how much longer would
it take for you to stop and how much
additional distance would you cover ?
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