PHYSICS- GRADE 11 AND GRADE 12 (MODE2)
Application of motion ,Force and Motion
Learning objective:
Motion Along a Straight Line
Motion in Two and Three Dimensions
PROJECTILE MOTION
UNIFORM CIRCULAR MOTION
RELATIVE MOTION IN ONE DIMENSION
RELATIVE MOTION IN TWO DIMENSIONS
Force and Motion—I
Motion Along a Straight Line
Graphical Integration in Motion Analysis
Integrating Acceleration. When we have a graph of an object’s acceleration a versus
time t, we can integrate on the graph to find the velocity at any given time. Because a is
defined as a dv/dt, the Fundamental Theorem of Calculus tells us that
……….1
The right side of the equation is a definite integral (it gives a numerical result rather
than a function), v0 is the velocity at time t0, and v1 is the velocity at later time t1. The
definite integral can be evaluated from an a(t) graph,
…….2
2
If a unit of acceleration is1 m/s and a unit of time is 1 s, then the corresponding unit of
area on the graph is1 m/s 2.
…………3
which is (properly) a unit of velocity. When the acceleration curve is above the time axis,
the area is positive; when the curve is below the time axis, the area is negative.
Integrating Velocity.
Similarly, because velocity v is defined in terms of the position x as v dx/dt, then
……….4
, where x0 is the position at time t0 and x1 is the position at time t1. The definite integral
on the right side of Equation can be evaluated from a v(t) graph, like that shown in
Figure. In particular
…………5
If the unit of velocity is 1 m/s and the unit of time is 1 s, then the corresponding unit of
area on the graph is
……….6
which is (properly) a unit of position and displacement. Whether this area is positive or
negative is determined as described for the a(t) curve.
APPLICATION
Graphical integration a versus t, whiplash injury
Whiplash injury” commonly occurs in a rear-end collision where a front car is hit from behind
by a second car. In the 1970s, researchers concluded that the injury was due to the occupant’s
head being whipped back over the top of the seat as the car was slammed forward. As a result
of this finding, head restraints were built into cars, yet neck injuries in rear- end collisions
continued to occur.
In a recent test to study neck injury in rear-end collisions, a volunteer was strapped to a seat
that was then moved abruptly to simulate a collision by a rear car moving at 10.5 km/h. Figure
2-15a gives the accelerations of the volunteer’s torso and head during the collision, which
began at time t = 0. The torso acceleration was delayed by 40 m/s because during that time
interval the seat back had to compress against the volunteer. The head acceleration was
,delayed by an additional 70 m/s. What was the torso speed when the head began to
accelerate?
Answer: First We Will Calculate the Torso Speed Combining Equation 1 and 2 of the Graphical
Integration
………6
For convenience, let us separate the area into three regions from 0 to 40 m/s, region A has no
area: A=0 From 40 m/s to 100 m/s, region B has the shape of a triangle, with area
From 100 m/s to 110 m/s, region C has the shape of a rectangle, with area
Substituting every values in equation 6
Time for full up-down flight, baseball toss
, Drag race of car and motorcycle
A popular web video shows a jet
airplane, a car, and a motorcycle
racing from rest along a runway (Fig.
2-10). Initially the motorcycle takes
the lead, but then the jet takes the
lead, and finally the car blows past
the motorcycle. Here let’s focus on the car and motorcycle and assign some reasonable values
to the motion. The motorcycle first takes the lead because its (constant) acceleration a(m)=8.40
m/s 2is greater than the car’s (constant) acceleration a(c)= 5.60 m/s 2, but it soon loses to the car
because it reaches its greatest speed v(m)= 58.8 m/s before the car reaches its greatest speed
v(c)= 106 m/s. How long does the car take to reach the motorcycle?
Application of motion ,Force and Motion
Learning objective:
Motion Along a Straight Line
Motion in Two and Three Dimensions
PROJECTILE MOTION
UNIFORM CIRCULAR MOTION
RELATIVE MOTION IN ONE DIMENSION
RELATIVE MOTION IN TWO DIMENSIONS
Force and Motion—I
Motion Along a Straight Line
Graphical Integration in Motion Analysis
Integrating Acceleration. When we have a graph of an object’s acceleration a versus
time t, we can integrate on the graph to find the velocity at any given time. Because a is
defined as a dv/dt, the Fundamental Theorem of Calculus tells us that
……….1
The right side of the equation is a definite integral (it gives a numerical result rather
than a function), v0 is the velocity at time t0, and v1 is the velocity at later time t1. The
definite integral can be evaluated from an a(t) graph,
…….2
2
If a unit of acceleration is1 m/s and a unit of time is 1 s, then the corresponding unit of
area on the graph is1 m/s 2.
…………3
which is (properly) a unit of velocity. When the acceleration curve is above the time axis,
the area is positive; when the curve is below the time axis, the area is negative.
Integrating Velocity.
Similarly, because velocity v is defined in terms of the position x as v dx/dt, then
……….4
, where x0 is the position at time t0 and x1 is the position at time t1. The definite integral
on the right side of Equation can be evaluated from a v(t) graph, like that shown in
Figure. In particular
…………5
If the unit of velocity is 1 m/s and the unit of time is 1 s, then the corresponding unit of
area on the graph is
……….6
which is (properly) a unit of position and displacement. Whether this area is positive or
negative is determined as described for the a(t) curve.
APPLICATION
Graphical integration a versus t, whiplash injury
Whiplash injury” commonly occurs in a rear-end collision where a front car is hit from behind
by a second car. In the 1970s, researchers concluded that the injury was due to the occupant’s
head being whipped back over the top of the seat as the car was slammed forward. As a result
of this finding, head restraints were built into cars, yet neck injuries in rear- end collisions
continued to occur.
In a recent test to study neck injury in rear-end collisions, a volunteer was strapped to a seat
that was then moved abruptly to simulate a collision by a rear car moving at 10.5 km/h. Figure
2-15a gives the accelerations of the volunteer’s torso and head during the collision, which
began at time t = 0. The torso acceleration was delayed by 40 m/s because during that time
interval the seat back had to compress against the volunteer. The head acceleration was
,delayed by an additional 70 m/s. What was the torso speed when the head began to
accelerate?
Answer: First We Will Calculate the Torso Speed Combining Equation 1 and 2 of the Graphical
Integration
………6
For convenience, let us separate the area into three regions from 0 to 40 m/s, region A has no
area: A=0 From 40 m/s to 100 m/s, region B has the shape of a triangle, with area
From 100 m/s to 110 m/s, region C has the shape of a rectangle, with area
Substituting every values in equation 6
Time for full up-down flight, baseball toss
, Drag race of car and motorcycle
A popular web video shows a jet
airplane, a car, and a motorcycle
racing from rest along a runway (Fig.
2-10). Initially the motorcycle takes
the lead, but then the jet takes the
lead, and finally the car blows past
the motorcycle. Here let’s focus on the car and motorcycle and assign some reasonable values
to the motion. The motorcycle first takes the lead because its (constant) acceleration a(m)=8.40
m/s 2is greater than the car’s (constant) acceleration a(c)= 5.60 m/s 2, but it soon loses to the car
because it reaches its greatest speed v(m)= 58.8 m/s before the car reaches its greatest speed
v(c)= 106 m/s. How long does the car take to reach the motorcycle?
