In physics, there are already derived equation that are based on Newton's Law of Motions. The rectilinear motions at constant acceleration have the following equations:
x = v₁t + 1/2 at²
a = (v₂-v₁)/t
where
x is the distance travelled
v₁ is the initial velocity
v₂ is the final velocity
a is the acceleration
t is the time
Now, we solve first the second equation. Since it mentions that the car comes eventually to a stop, v₂ = 0. Then,
-5 = (0-v₁)/t
-5t = -v₁
v₁ = 5t
We use this new equation to substitute to the first one:
x = v₁t + 1/2 at²
15 = 5t(t) + 1/2(-5)t²
15 = 5t² - 5/2 t²
15 = 5/2 t²
5t² = 30
t² = 30/5 = 6
t = √6 = 2.45
Therefore, the time it took to travel 15 m at a deceleration of -5 m/s² is 2.45 seconds.
Answer:
1.04%
Explanation:
Given that,
The power of drill = 3.5 kW = 3500 W
Transferred kinetic energy = 5000 kJ during 15 seconds of use.
We need to find the percentage efficiency of the drill. It can be given by :
Where
Po and Pi are output and input powers.
So,
So, the percentage efficiency of the drill is 1.04%.
Answer:
When the ball hits the ground, its velocity is -128 ft/s.
Explanation:
Hi there!
First, let's find the time it takes the ball to reach the ground (the value of t for which s(t) = 0):
s(t) = -16t² + 32t + 240
0 = -16t² + 32t + 240
Solving the quadratic equation with the quadratic formula:
t = 5.0 s (the other solution of the equation is rejected because it is negative).
Now, we have to find the velocity of the ball at t = 5.0 s.
The velocity of the ball is the change of height over time (the derivative of s(t)):
v = ds/dt = s'(t) = -32t + 32
at t = 5.0 s:
s'(5.0) = -32(5.0) + 32 = -128 ft/s
When the ball hits the ground, its velocity is -128 ft/s.
The term Milankovitch cycles most closely relate to periodic
changes in Earth’s orbit and angle of tilt relative to sun. So for this
question, the correct option is option “c”. Milankovitch affects actually deals
with the effect of the changes in the earth’s movements with the change in the
climatic conditions. Milankovitch was a Serbian geophysicist and also a great
astronomer. His studies actually helped in relating the climatic changes with
the changes in the tilt of the earth. He was the first person to mathematically
prove this situation.
