Unit 2 Test Review

Relative Motion Remember the truck problem – Consider systems moving together as a sub system. A police car is chasing a criminal who is driving at 70 mi/hr and at the exact same speed as the police. The police decides to overtake the criminal, maintaining a minimum distance of 3 m before and after the pass. How long does it take the police to overtake if the criminal’s pickup truck is 4 m long.

At time t = 0, car X traveling with speed v0 passes car Y At time t = 0, car X traveling with speed v0 passes car Y. which is just starting to move. Both cars then travel on two parallel lanes of the same straight road. The graphs of speed v versus time t for both cars are shown above. Which of the following is true at time t = 20 seconds? Both cars have the same acceleration. Car Y is in front of car X. Car Y is behind car X. Car X is accelerating faster then car Y. Car Y is passing car X.

Average Velocity Vs. Instantaneous Avg V = Total Displacement/ Total Time Avg S = Total Distance/ Total Time Ins V = V at a moment or a particular time Ins S = S at a moment or a particular time

Calculus usage for finding x, v or a as a function of time Position Area/ Integrate Velocity function within time interval Slope / Differentiate the Position function Velocity Area/ Integrate Acceleration function within time interval Slope / Differentiate the Velocity function Acceleration

Constant Velocity and Acceleration Constant Velocity - it is the simplest case of motion ( and kinda boring !!) - Velocity = Displacement/ Time - Speed = Distance / Time - Acceleration = 0 Constant Acceleration( V-t is straight line) - Has 4 basic equations

Think about V0 and a for various situations

Know your graphs well

A box slides down a frictionless inclined plane with an acceleration equal to horizontal component of earth’s gravity and is = ‘g Sinθ ‘ .What effect does the vertical component of g (=‘g Cosθ’) have on the box? b) Is there a limit to how high the vertical component can be? c) How does nature of inclined plane material affect g Cosθ effect? e.g. cushy foam plane? Inclined Plane g Sinθ 90 - θ g g Cosθ θ

Racing a cart down a ramp. A cart is just released from the top of a frictionless ramp which is 5 m long. How long does it take for the cart to reach the ground and with what is it’s velocity at the bottom of the ramp ?

A 3.0 m long board has one end raised to a height of 60 cm to form an incline. A 4.0 kg mass is allowed to slide without friction down the entire length of the inclined plane. a. What is the final speed of the mass when it reaches the bottom ? b. If the mass is replaced with an 8.0 kg mass, what would be the new speed when it reaches the bottom?

The box is released from rest at the top of the incline, and its speed after it has traveled 6.00 m to the bottom of the incline is 4.00 m/s . What is the speed of the block when it is 5.00 m from the top of the incline?

Practice Problems An object moving in a straight line has a velocity v in meters per second that varies with time t in seconds according to the following function. v = 3.6 + 3.59 t The displacement of the object between t = 0 and t = 8.7 seconds is ______________meters

1. The cart moves away from the detector, speeding up. Practice Problems For each of the situations below, draw your prediction of what the acceleration versus time graph for the motion that is described in each case will look like. Help on Drawing 1. The cart moves away from the detector, speeding up. 2. The cart moves away from the detector, slowing down. 3. The cart moves toward the detector, speeding up.

The object will reverse its direction of travel at the origin. Practice Problems An object moves in the +x direction at a speed of 35 m/s. As it passes through the origin, it starts to experience a constant acceleration of 4.0 m/s2 in the -x direction. What will happen next? The object will travel in the +x direction and then reverse its direction. The object will reverse its direction of travel at the origin. The object will keep traveling in the +x direction. (b) How much time elapses before the object returns to the origin? (c) What is the velocity (magnitude and direction) of the object when it returns to the origin?

Practice Problems A car traveling in a straight -line path has a velocity of +24.60 m/s at some instant. After 5.67 s, its speed is +5.44 m/s. What is its average acceleration (in m/s/s) during this time interval? 2. A car traveling initially at +6.14 m/s accelerates at the rate of 0.755 m/s/s for a time of 7.79 s. What is its velocity (in m/s) at the end of the acceleration? 3. A tennis ball with a speed of 9.18 m/s is thrown perpendicularly at a wall. After striking the wall, the ball rebounds in the opposite direction with a speed of 6.80 m/s. If the ball is in contact with the wall for 0.0011 s, what is the value of the average acceleration (in m/s/s) of the ball while in contact with the wall? 4. A particle moves along the x axis with a non-constant acceleration described by a = 12t, where a is in meters per second squared and t is in seconds. If the particle starts from rest so that its speed v and position x are zero when t = 0, where is it located when t = 2 seconds?