Suppose you are driving a car. let s(t) denote your position in feet at time t (and assume s(t) is differentiable). consider an interval of time [ 0, 40 ] (in seconds). at t = 0, you put your foot on the pedal softly and keep the same amount of force on the pedal for 10 seconds. at the 10 second mark, you begin increasing the force of your foot gradually until t = 20, when you see a red light in the distance, so you gradually lift your foot from the pedal. at t = 30, you begin braking, and finally stop at the red light at t = 40. at what time t does the sign of the second derivative switch from positive to negative or from negative to positive?

at t=20 the second derivative switches from positive to negative

Explanation:

s(t) denotes the position in time

s'(t) the first derivative denotes the speed in time

s''(t) the second derivative, the one we want denotes the acceleration

From T=0 to T=10 the acceleration is 0.

From T=10  to T=20 the acceleration is positive

at T=20 the acceleration switches from positive to negative

at T=30 the acceleration becomes even more negative

and at T=40 the acceleration becomes 0

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:

f=ma newton

f=100x2.5=250n