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Applications of Integration: Position, Velocity and Acceleration
Related Topics
Wize University Calculus 1 Textbook > Applications of Integration for Physical Science
Position, Velocity, and Acceleration
4 Activities
If an object is dropped off a 100-meter cliff, find its average velocity (to two decimal places) over the time it is dropped to the time it hits the ground.
Answer
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Check Submission
More Position, Velocity, and Acceleration Questions:
Applications of Integration: Position from Acceleration
The position of an object is given by
x
(
t
)
x(t)
x
(
t
)
. If its acceleration is given by
a
(
t
)
=
6
t
−
2
a(t)=6t-2
a
(
t
)
=
6
t
−
2
m/s
2
and if it starts from
x
(
0
)
=
1
x(0)=1
x
(
0
)
=
1
m with a velocity
v
(
0
)
=
2
v(0)=2
v
(
0
)
=
2
m/s, where will the object be at
t
=
2
t=2
t
=
2
?
Applications of Integration: Position from Acceleration
The position of an object is given by
x
(
t
)
x(t)
x
(
t
)
. If its acceleration is given by
a
(
t
)
=
6
t
−
2
a(t)=6t-2
a
(
t
)
=
6
t
−
2
m/s
2
and if it starts from
x
(
0
)
=
1
x(0)=1
x
(
0
)
=
1
m with a velocity
v
(
0
)
=
2
v(0)=2
v
(
0
)
=
2
m/s, where will the object be at
t
=
2
t=2
t
=
2
?
A clown is shot directly up out of a cannon with a velocity of
50
m
/
s
50\ m/s
50
m
/
s
. If gravity causes a
−
10
m
/
s
2
-10 \ m/s^2
−
10
m
/
s
2
constant acceleration, how high is the clown
2
2
2
seconds later?
Applications of Integration: Position, Velocity and Acceleration
Suppose a car hits the brakes at full power and comes to a complete stop after 50 meters. Assuming that the deceleration caused by the brakes is a constant
−
10
m/sec
2
-10 \text{ m/sec}^2
−
10
m/sec
2
, find the speed of the car (in meters per second, to two decimal places) when it began braking.
Applications of Integrals: Position, Velocity and Acceleration
Suppose a coin is dropped off the side of a 50 meter tall cliff. Find the
speed
of the coin when it hits the ground (to two decimal places) in meters per second.
Applications of Integration: Position from Acceleration
The position of an object is given by
x
(
t
)
x(t)
x
(
t
)
. If its acceleration is given by
a
(
t
)
=
6
t
−
2
a(t)=6t-2
a
(
t
)
=
6
t
−
2
m/s
2
and if it starts from
x
(
0
)
=
1
x(0)=1
x
(
0
)
=
1
m with a velocity
v
(
0
)
=
2
v(0)=2
v
(
0
)
=
2
m/s, where will the object be at
t
=
2
t=2
t
=
2
?
Kinematics
The following graph represents the velocity of a particle in m/s, find the total displacement in meters of the particle from t=0 to t=5.
Related Rates
A clown is shot directly up out of a cannon with a velocity of
50
m
/
s
50\ m/s
50
m
/
s
. If gravity causes a
−
10
m
/
s
2
-10 \ m/s^2
−
10
m
/
s
2
constant acceleration, how high is the clown
2
2
2
seconds later?
Applications of Integration: Position, Velocity and Acceleration
A sky diver with a broken parachute falls at a constant acceleration
of
−
10
m
/
s
2
-10 \ m/s^2
−
10
m
/
s
2
. He passes a bird at
1000
m
1000 \ m
1000
m
of altitude at a speed of
100
m
/
s
100\ m/s
100
m
/
s
.
(a) How fast is he moving
10
10
10
seconds later?