Answer:
Tt = 70 + 135e^-0.031t
13 minutes
Explanation:
Given that :
Initial temperature, Ti = 205°
Temperature after 2.5 minutes = 195°
Temperature of room, Ts= 70
Using the relation :
Tt = Ts + Ce^-kt
Temperature after time, t
When freshly poured, t = 0
205 = 70 + Ce^-0k
205 = 70 + C
C = 205 - 70 = 135°
T after 2.5 minutes to find proportionality constant, k
Tt = Ts + Ce^-kt
195 = 70 + 135e^-2.5k
125 = 135e^-2.5k
125 / 135 = e^-2.5k
0.9259 = e^-2.5k
Take In of both sides :
−0.076989 = - 2.5k
k = −0.076989 / - 2.5
k = 0.031
Equation becomes :
Tt = 70 + 135e^-0.031t
t when Tt = 160
160 = 70 + 135e^-0.031k
90 = 135e^-0.031t
90/135 = e^-0.031t
0.6667 = e^-0.031t
In(0.6667) = - 0.031t
−0.405465 = - 0.031t
t = 0.405465/ 0.031
t = 13.071
t = 13 minutes
Near Greenland in the northern hemisphere <span />
B. The apple from the bottom will hit the ground earlier. This is because an increase in height causes an increase in the time that the object will fall, and therefore will affect the final velocity of the falling object. Moreover, the reduction in velocity due to friction from the air should also be considered.
b. describes it best because a form of molten cools down and makes igneous rock. Good luck! Please mark me brainliest!
Answer:
Momentum is given by
p
=
m
v
. Impulse is the change of momentum,
I
=
Δ
p
and is also equal to force times time:
I
=
F
t
. Rearranging,
F
=
I
t
=
Δ
p
t
=
0
−
20
,
000
5
=
−
4000
N
.
Explanation:
Momentum before the collision is
p
=
m
v
=
2000
⋅
10
=
20
,
000
k
g
m
s
−
1
.
Assuming the truck comes to a complete halt, the momentum after the collision is
0
k
g
m
s
−
1
.
The change in momentum,
Δ
p
, is initial minus final
→
0
−
20
,
000
=
−
20
,
000
This is called the impulse:
I
=
Δ
p
. Impulse is also equal (check the units) to force times time:
I
=
F
t
.
We can rearrange this expression to make
F
the subject:
F
=
I
t
=
Δ
p
t
=
−
20
,
000
5
=
−
4000
N
The negative sign just means the force acting is in the opposite direction to the initial momentum.
(This will be the average force acting during the collision: collisions are chaotic so the force is unlikely to be constant.)