#### Kinematics

4. Define discrete and continuous modeling

Q4

3. A particle performs a simple harmonic motion given by the equation: At t=0.80 s find: (a) the position of the particle. b) the velocity of the particle. c) the acceleration of the particle. d) the kinetic, potential and total energy of the system, if the mass is 0.120 kg.

4. Consider a vertical mass-spring system. The spring constant is k = 48N/M and he mass is m = 1.0 kg. a) Find the angular frequency. The mass is pulled from equilibrium 0.10 m down. b) Write the equation for the displacement as a function of time, with a vertical x axis is pointing upward.

2. Diesel tends to wait until the rabbit is closest before starting to chase. If the rabbit is traveling across the yard in a straight line, we can assume the simulation will start when the rabbit is located at [x (0), y (0)] = [x, 0] and have a velocity of [x` (0), y` (0)] = [0, C ], where RRO RRR CR is the maximum speed at which the rabbit can run. Note, we are ignoring acceleration here, we are just assuming the rabbit has already accelerated to it's max velocity and stays there. So, the velocity vector can change direction, but not magnitude. And the rabbit will change direction, so the velocity will change direction. From my observation, it does so when Diesel gets within a certain distance of the rabbit. But to keep it simple, suppose the rabbit just turns 90 degrees to the right at a fix rate of 90 degrees/second starting at t = 2. Write the equations for the rabbit's velocity, i.e. x' (t) and y' (t). RR

Question 1 to 8 - mcq

4. A car crashes into a brick wall at a speed of 120.0 km/h, so that the driver (mass 63 kg) travels 40.0 cm before stopping. Determine the average force applied to the driver.

1. What is the efficiency of a kettle that uses 1.0 x 10³ Watts of power to heat 0.50 kg of water from 24° C to 100° C in 4.0 minutes? (cater=4180 J/kg °C)

2. A 68.2 kg diver drops off a diving board that is 16.8m above the water surface. If the force of air resistance acting on the diver is 121 N [UP] determine: a. The work done by gravity on the diver during the jump b. The work done by air resistance on the diver during the jump c. The speed of the diver as they hit the water

3. ***A roller coaster of mass 1.35 x 10³kg rides on the track shown. It starts with a speed of 6.0 m/s at point A. a. Calculate the maximum speed (friction can be ignored) and state at what point it happens. b. Calculate the speed of the roller coaster at point E c. If the maximum speed the roller coaster can safely have at point C is 50 m/s, what is the maximum height that point A could have? (you can assume initial speed at point A is still 6.0 m/s) A Ast 100. m E D 38 m B 20. m