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Applications of Integration: Position from Acceleration
Related Topics
Wize University Calculus 1 Textbook > Applications of Integration for Physical Science
Position, Velocity, and Acceleration
4 Activities
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
?
x
(
2
)
=
x(2)=
x
(
2
)
=
I don't know
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, Velocity and Acceleration
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.
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?