The speed of the cart after 3 seconds of Low fan speed is equal to 54 cm/s.
<h3>How to calculate the speed?</h3>
Mathematically, speed can be calculated by using this formula;
Speed = distance/time
At Low fan speed after 3 seconds, the distance covered is 162 cm:
Speed = 162/3
Speed = 54 cm/s.
At Medium fan speed after 5 seconds, the distance covered is 600 cm:
Speed = 600/5
Speed = 120 cm/s.
At High fan speed after 2 seconds, the distance covered is 128 cm:
Speed = 128/2
Speed = 64 cm/s.
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-GMm/2r is the total energy of the mass m if it is in a circular orbit about mass M.
Given
A particle of mass m moving under the influence of a fixed mass's M, gravitational potential energy of formula -GMm/r, where r is the separation between the masses and G is the gravitational constant of the universe.
As the Gravity Potential energy of particle = -GMm/r
Total energy of particle = Kinetic energy + Potential Energy
As we know that
Kinetic energy = 1/2mv²
Also, v is equals to square root of GM/r
v = √GM/r
Put the value of v in the formula of kinetic energy
We get,
Kinetic Energy = GMm/2r
Total Energy = GMm/2r + (-GMm/r)
= GMm/2r - GMm/r
= -GMm/2r
Hence, -GMm/2r is the total energy of the mass m if it is in a circular orbit about mass M.
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Kinetic Energy = 1/2mv^2
m= 1200kg
v= 24 m/s
KE = 1/2 (1200kg)(24m/s)^2 = 345,600 N
Firstly, we must find the equation the speed, it can be obtained by the derivative of x =<span>x = 4.0t2 - 32t + 36, it means v= 8.0t-32. the particule stops means v= 0, and 0= 8.0t-32, which implies 8t=32, so t=4s, and then x(t=4) = 4.0(4)^2 - 32(4) + 36= - 28m
so x = - 28 m</span>
