A car in a roller coaster moves along a track that consists of a sequence of ups and downs. Let the x axis be parallel to the ground and +y axis point upward. In the time interval from t=0 to t=4 s the trajectory of the caralong a certain section of the track is given by
→r=A(1 m/s)t^i+A((1 m/s3)t3−6(1 m/s2)t2)^j, where A is positive dimensionless constant. a. At t=2.0s is the roller coaster car ascending or descending?
b. Derive a general expression for the speed v of the car. Make sure that your expression would give the correct value for the speed (in m/s), but you don't need to put in anything explicitly about units (unlike what you see in the original expressionfor →r. Express your answer in meters per second in terms of A and t.

Explanation:

r=A(1 m/s)t^i+A((1 m/s3)t3−6(1 m/s2)t2)^j,

dr / dt = A i  + (3 A t² - 6 x 2 t ) j

At t = 2

dr / dt = A i  + (12A - 24 A ) j  = A i - 12 A j .

Since slope is negative so velocity is downwards , hence it is descending

b ) velocity = dr / dr =  .  A i  + (3 A t² - 6 x 2 t ) j

Vx = A

Vy = 3A t² - 12 t

low freq = 100 mhz

low wavelength =101.7m

length = 3x10^8/freq

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation: