Solution:
h,t...full falling path,time
h2,t2...path,time in last second
h1...rest of path
h1+h2=h
h1=h2=h/2
January 31, 2008
Free fall
During the last second of free fall object pass half of the full length of falling path. From which height and how long did the object fall?
Solution:
h,t...full falling path,time
h2,t2...path,time in last second
h1...rest of path
h1+h2=h
h1=h2=h/2
Solution:
h,t...full falling path,time
h2,t2...path,time in last second
h1...rest of path
h1+h2=h
h1=h2=h/2
January 30, 2008
Simple acceleration example
One car can accelerate from 0 to 100 kmh-1 in 9 sec. Calculate acceleration and path if acceleration is constant.
v1=0 kmh-1
v2=100 kmh-1 =27,78 ms-1
t=9,0 sec
Solution:
where s is distance of car from starting position.
In reality car does not accelerate constantly, and with this example we calculated mid acceleration.
v1=0 kmh-1
v2=100 kmh-1 =27,78 ms-1
t=9,0 sec
Solution:
where s is distance of car from starting position.
In reality car does not accelerate constantly, and with this example we calculated mid acceleration.
January 23, 2008
Meeting problem
In 17h 33 min train In Paris (France) started moving toward Madrid (Spain) with velocity 140 km/h, while second train in 18h 0min started moving from Madrid toward Paris with velocity 120 km/h. Distance between Paris and Madirid is 1100 km. When and where will theese trains meet?
d=1100 km
v1=140 km/h
v2=120 km/h
t1=17h 33min
t2=18h 00min
Solution:
Trains will meet in time t far s1 from Paris. In the meeting time first train will pass s1=v1(t-t1), while the second train is far from initial position s2=v2(t-t2).
These two paths together make distance d: s1+s2=d whic makes
v1t-v1t1+v2t-v2t-v2t2=d
t=17h 33 min+ 4h 26 min = 21h 59 min
Place of meeting is far from Paris:
s1=v1(t-t1) =621,32 km
d=1100 km
v1=140 km/h
v2=120 km/h
t1=17h 33min
t2=18h 00min
Solution:
Trains will meet in time t far s1 from Paris. In the meeting time first train will pass s1=v1(t-t1), while the second train is far from initial position s2=v2(t-t2).
These two paths together make distance d: s1+s2=d whic makes
v1t-v1t1+v2t-v2t-v2t2=d
t=17h 33 min+ 4h 26 min = 21h 59 min
Place of meeting is far from Paris:
s1=v1(t-t1) =621,32 km
January 18, 2008
Overtake problem
One truck which is long 6m, velocity 80 km/h started overtaking another truck which is 15m long and with velocity 65 km/h. How long does overtaking last, and how far is faster truck from initial postition if overtaking starts and ends when two trucks are at distance 30m?
Solution:
d1=6m
v1=80 km/h
d2=15m
v2=65 km/h
d=30 m
When slower truck pass path s2=v2t, faster car pass:
s1=v1t=d+d2+v2t+d+d1
from which we can calculate t,
Faster car from his initial position pass:
s1=v1t=432 m
We can see that if relative speed v1-v2 is less overtaking time is growing.
Solution:
d1=6m
v1=80 km/h
d2=15m
v2=65 km/h
d=30 m
When slower truck pass path s2=v2t, faster car pass:
s1=v1t=d+d2+v2t+d+d1
from which we can calculate t,
Faster car from his initial position pass:
s1=v1t=432 m
We can see that if relative speed v1-v2 is less overtaking time is growing.
January 15, 2008
Linear motion
When object is displacing during a time interval average velocity is described by formula
If we want to calculate instantaneous velocity at one point we must make time interval small (infinite small)
SI unit for velocity is meters/seconds (ms-1).
In the case of linear motion and constant velocity we can write formula (1) as
where s is path traveled during time t. We also have
Acceleration is defined as rate of change of velocity
In SI units, acceleration is measured in meters/seconds2 (ms-²)
Special way of motion is when a=const. in which case we have:
v=v0+at,
s=v0t+at2/2,
v2=2as+v02,
where v0 is starting speed and path s is measured from time t=0. When object is speeding up value of a is positive and if object is slowing down value of acceleration 'a' is negative.
In free fall which is one of the important movements where a=const. acceleration is labeled as g and in numerical problems we calculate as g=9,81 ms-2.
Displacement, velocity and acceleration are vectors which because of simplicity they were written as scalars.
If we want to calculate instantaneous velocity at one point we must make time interval small (infinite small)
SI unit for velocity is meters/seconds (ms-1).
In the case of linear motion and constant velocity we can write formula (1) as
where s is path traveled during time t. We also have
Acceleration is defined as rate of change of velocity
In SI units, acceleration is measured in meters/seconds2 (ms-²)
Special way of motion is when a=const. in which case we have:
v=v0+at,
s=v0t+at2/2,
v2=2as+v02,
where v0 is starting speed and path s is measured from time t=0. When object is speeding up value of a is positive and if object is slowing down value of acceleration 'a' is negative.
In free fall which is one of the important movements where a=const. acceleration is labeled as g and in numerical problems we calculate as g=9,81 ms-2.
Displacement, velocity and acceleration are vectors which because of simplicity they were written as scalars.
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