A toy car with a mass m is accelerated in a hallway with a force that varies uniformly from 0 Newtons to three times the weight of the car over a timet. At that point, the engine shuts down, and the car continues to travel at a constant
speed along the hallway for a time equal tot.
This hall can be considered to be frictionless from the start of the trip to this position. After time 2t has passed, the
car reaches a rough surface with a force of friction equal to 0.5 mg and continues along this surface until timet
when the car comes to rest.
a. Create a graph of Force vs. Time for the entire trip of the car.
b. Calculate the impulse given the car by the engine during the time when the force acts, t.
c. Calculate the momentum lost by the car during the time when the force of friction is acting.
d. Calculate the total time until the car stops.

After a big snowfall, you take your favorite rocket-powered sled out to a wide field. the field is 195 m across, and you know that your sled accelerates at a rate of 3.65 m/s2 when the rocket is on. how much time will it take the sled to cross the field starting from rest, assuming the rocket is on the whole time?

If vx = 7.00 units and vy = -7.60 units, determine the magnitude of v⃗ . determine the direction of v⃗ .

The particle in a two-dimensional well is a useful model for the motion of electrons around the indole ring (3), the conjugated cycle found in the side chain of tryptophan. we may regard indole as a rectangle with sides of length 280 pm and 450 pm, with 10 electrons in the conjugated p system. as in case study 9.1, we assume that in the ground state of the molecule each quantized level is occupied by two electrons. (a) calculate the energy of an electron in the highest occupied level. (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels. 9.27 electrons around the porphine ring (4), the conjugated macrocycle that forms the structural basis of the heme group and the chlorophylls. we may treat the group as a circular ring of radius 440 pm, with 20 electrons in the conjugated system moving along the perimeter of the ring. as in exercise 9.26, assume that in the ground state of the molecule quantized each level is occupied by two electrons. (a) calculate the energy and angular momentum of an electron in the highest occupied level. (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels.