Answer:
it tells you that the speed increases until about 20 seconds then keeps a steady pace for 20 seconds then the speed drops and stops at 55 seconds in the process.
Answer:
v=9.6 km/s
Explanation:
Given that
The mass of the car = m
The mass of the truck = 4 m
The velocity of the truck ,u= 12 km/s
The final velocity when they stick = v
If there is no any external force on the system then the total linear momentum of the system will be conserve.
Pi = Pf
m x 0 + 4 m x 12 = (m + 4 m) x v
0 + 48 m = 5 m v
5 v = 48
v=9.6 km/s
Therefore the final velocity will be 9.6 km/s.
Imagine a right triangle where the legs represent the horizontal and vertical lengths of the string and the hypotenuse represents the length of the string.
Let us assign some values:
x = horizontal length in feet
50 = vertical length in feet
L = length of the string in feet
Because we are modeling these quantities with a right triangle, we can use the Pythagorean theorem to relate them with the following equation:
L² = x² + 50²
We want to find an equation for the change of L over time, so first differentiate both sides with respect to time t then solve for dL/dt:
2L(dL/dt) = 2x(dx/dt)
dL/dt = (x/L)(dx/dt)
First let's solve for x at the moment in time described in the problem using the Pythagorean theorem:
L² = x² + 50²
Given values:
L = 100ft
Plug in and solve for x:
100² = x² + 50²
x = 86.6ft
Now let's find dL/dt. Given values:
x = 86.6ft, L = 100ft, dx/dt = 4ft/sec
Plug in and solve for dL/dt:
dL/dt = (86.6/100)(4)
dL/dt = 3.46ft/sec
Answer:
A voltage is an electromotive force or potential difference expressed in volts. A potential difference is the difference of electrical potential between two points
Answer:
<h2>0.245cm/min</h2>
Explanation:
The volume of the spherical balloon is expressed as V = 4/3πr³ where r is the radius of the spherical balloon. If the spherical balloon is inflated with gas at the rate of 500 cubic centimetres per minute then dV/dt = 500cm³.
Using chain rule to express dV/dt;
dV/dt = dV/dr*dr/dt
dr/dt is the rate at which the radius of the gallon is increasing.
From the formula, dV/dr = 3(4/3πr^3-1))
dV/dr = 4πr²
dV/dt = 4πr² *dr/dt
500 = 4πr² *dr/dt
If radius r = 40;
500 = 4π(40)² *dr/dt
500 = 6400π*dr/dt
dr/dt = 500/6400π
dr/dt = 5/64π
dr/dt = 0.245cm/min
Hence, the radius of the balloon is increasing at the rate of 0.245cm/min
