Answer:
Explanation:
Given equation is ,
x =t + 2 t³ ,
dx/dt = velocity ( v ) = 1 + 6 t²
a) kinetic energy = 1/2 m v² = .5 x 4 ( 1 + 6 t² )² = 2 ( 1 + 6 t²)²
b ) Acceleration = dv /dt = 12 t .
force( F ) = mass x acceleration = 4 x 12 t = 48 t
Power = force x velocity = 48 t x ( 1 + 6 t²). = 48 t + 288 t³ )
work done = ∫ F dx =∫ 48 t x( 1 + 6t² )dt ; = [48t²/2 + 48 x 6 x t³ /3 = 24 t² + 96 t³ )]₀² = 864 J
Answer:
Explanation:
mass of probe m = 474 Kg
initial speed u = 275 m /s
force acting on it F = 5.6 x 10⁻² N
displacement s = 2.42 x 10⁹ m
A )
initial kinetic energy = 1/2 m u² , m is mass of probe.
= .5 x 474 x 275²
= 17923125 J
B )
work done by engine
= force x displacement
= 5.6 x 10⁻² x 2.42 x 10⁹
= 13.55 x 10⁷ J
C ) Final kinetic energy
= Initial K E + work done by force on it
= 17923125 +13.55 x 10⁷
= 1.79 x 10⁷ + 13.55 x 10⁷
= 15.34 x 10⁷ J
D ) If v be its velocity
1/2 m v² = 15.34 x 10⁷
1/2 x 474 x v² = 15.34 x 10⁷
v² = 64.72 x 10⁴
v = 8.04 x 10² m /s
= 804 m /s
Answer:
200 N = 200 Newtons
Explanation:
Just use the formula F = m*a
F = Force in Newtons
m = mass and is 20 kg
a = acceleration and is 10 m/s^2
F = 20 * 10
F = 200 Newtons.
Free fall is a special case of motion with constant acceleration, because acceleration due to gravity is always constant and downward. For example, when a ball is thrown up in the air, the ball's velocity is initially upward.
Answer:
There are four different stages of sleep.
Stage 1 NREM
Explanation:
<em>The process of firmly falling asleep has four stages through which a person goes.</em>
<em>It goes from being awake over light sleep and falling firmly into sleeping.</em>
(STAGE 1)
This is a stage in which there are non-rapid movements of the eyes. In other words, it is a process of dreamless sleep. You enter this stage the moment you decide to sleep and shut your eyes. After several minutes, your body is in fact in the sleeping mode, but not entirely. This means that you can easily be woken up without being aware that you have slept.
Features:
- <em>You can easily awake</em>
- <em>Your may roll and they may be a little open</em>
- <em>The blood pressure and the temperature of the brain start to decrease </em>
- <em>You experience the natural human reflexes that the brain sends to assure that the place of your sleep is in a safe environment. By sending twitches to your muscles, your brain may awake your body for several seconds which comes in handy if you are tired and close to sleep on work or some dangerous place like a cliff for example.</em>
- <em>Your breading starts to slow down alongside with your pressure and temperature, and your heartbeats slow down.</em>
