Equations of Motion for Constant Resultant Force Also called because acceleration and resultant force are directly proportional s uvat equations Also called unhelpfully ID: 622796
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Slide1
Equations of Motion for Uniform AccelerationSlide2
Equations of Motion for Constant Resultant Force
Also called ….
because………
…acceleration and resultant force are directly proportional. Slide3
s
uvat
equations
Also called ….
(unhelpfully)
Unhelpful because it doesn’t tell us anything about when or how to apply themSlide4
s
uvat
equations
Also called ….
(unhelpfully)
s
– displacement
u – initial velocity
v – final velocity
a – uniform acceleration
t – time between u and v
Slide5
All of these are vectors therefore the sign of each one is very important
The equations have to be homogeneous so make sure your units are
Usually m, s, ms
-1 and ms
-2
s
– displacement
u – initial velocity
v – final velocity
a – uniform acceleration
t – time between u and v
Slide6
Let’s start with straight forward acceleration.
Acceleration = rate of change of velocity
Where’s Carl?
Be careful to get v and u the right way around
This is given on the formula sheet as
Slide7
Example using
A car slows
uniformly from
25 ms
-1
to 10 ms
-1
in 12 s. The car has a mass of 900 kg. What
constant force
do the brakes need to exert?
v
= 10 ms
-1
u
= 25 ms-1t = 12 s
ms
-2
i
.e. an acceleration of ms-2 in the opposite direction to motion 5 NFinal answer 1100 N in the opposite direction to motion
Slide8
Now displacement…consider the v-t graph
displacement = area under graph
but from
so
(at)
0 t
v
uSlide9
Example using
How far does the car in the previous example travel while under constant braking?
u
= 25 ms
-1
t
= 12 s
ms
-2
m
What happens if we forget the sign of the acceleration?
Slide10
Could we have worked this out without
a
?
Yes!
displacement (at constant acceleration) = average velocity x time
This is the same as before from the are under the graph:
Check it
Slide11
What if we don’t know how long the motion took?
Rearrange the acceleration formula to
and substitute into
Usually given as
Slide12
We can use this to find out how fast an object will be moving after it has been dropped from rest through a certain distance….
If you fall off a 100m high monument (in vacuum), how fast will you be moving when you hit the floor?Slide13
How do you know which one to use?
Write down what you DO know
a=
s=u=
etcWrite down what you want to find:v=?Look for the formula with JUST a, s, u and vSlide14
Summary - Equations of Motion for Uniform Acceleration
Get yourself a nice drawing
Define the positive direction and stick to it throughout
Write down what you know
Write down what you need to find outLook for the right equationCheck the units are consistent
Be careful with signs
Solve it
Reduce to a sensible number of significant figures
Don’t forget the units