20. A car starts from rest with an acceleration of 4.5 m/s². A half a minute later the acceleration stops, and the car continues at a constant velocity for 2.0 minutes. The car’s brakes are then applied, and the car comes to a stop in 1.0 minute. Show the car’s motion on a velocity vs. time graph.

Find the total displacement of the car. Clearly outline each interval, write out a plan for each interval, and clearly show the three different displacements before you add the total. (+ 22,275 m = +22,000 with corrrect sig digs).

Sketch what you think the corresponding displacement graph would look like for this situation. Keep in mind the rules for varying velocity and constant velocity.

Why can't you use distance equals rate times time in parts one and two of this problem?

A car starts at 60 m/s and slows to a certain speed over a distance of 400 m with an acceleration of 2.5 m/s². The car proceeds at that speed for a distance of 600 m, and then begins to speed up again to 50 m/s with an acceleration of .625 m/s². Find the total time of the trip by breaking this problem into three distinct sections again. (39 seconds).

Now that you know the time intervals, make a sketch of the car's motion using a velocity vs. time graph.

21. A car traveling at 30 m/s begins to slow down after passing a mile marker with an acceleration of 6.0 m/s². As soon as it comes to a stop, it immediately goes in reverse keeping the same acceleration. Find how far it will have traveled while coming to a stop. (75 m)

What is its displacement after 5.0 seconds? Why? (+ 75 m)

What is its displacement after 7.0 seconds? (+ 63 m)

Why is the last answer smaller than the displacement it traveled to a stop?

How long will it take the car to get back to the mile marker? (10 s)

If the car kept on going after it reached the mile marker, find its displacement after 15 seconds. (- 225 m = - 230 m with correct sig digs).

What does the negative mean in your last answer?

22. Find how long it would take a truck to go from a velocity of + 8.0 m/s to + 20 m/s if the acceleration + 1.2 m/s². (10 seconds)

What distance did the truck cover during that time? (140 m)

After traveling at 20 m/s, the truck begins to slow down with an acceleration of 1.5 m/s². Find the final velocity if the acceleration lasted 6.0 seconds. (+ 11 m/s)

What distance did the truck cover during this time? (93 M)

A police car leaves in pursuit of a holdup car .50 hours after the latter has left the scene of the crime at 120 mph. How fast must the police car go if it is to catch up with the holdup car in 1.0 hour? (This one will make you think). (180 mph)

23. A DC-8 airplane has a takeoff velocity of 80 m/s, which it reaches 35 s after starting from rest. How much time does the airplane spend in going from 0 to 20 m/s? (8.75 s)

What distance does it cover in doing so? (87.5 m)

How much time does the airplane spend in going from 60 to 80 m/s? (8.75 s)

Why is the time you just found the same time found in level one of this problem?

What distance does it cover in doing so? (612.5 m)

What is the necesarry minimum length of the runway for this particular plane? (+ 1400 m)

24. A golf cart has an acceleration of 0.4 m/s². What is its velocity after it has covered 10.0 m starting from rest? (+ 2.8 m/s)

If the cart maintained that acceleration, how far would it go if it reached a velocity of + 6.0 m/s? (35 m)

Find the cart's new acceleration if it went from + 6.0 m/s to + 4.0 m/s and covered 5.0 meters in the process. (- 2.0 m/s²)

Find how long it took the cart to slow to + 4.0 m/s (from the last level). (1.0 s)

25. A Ferrari covers a 100-m from a standing start in 6.0 s with a constant acceleration. Find its final velocity. (+ 33 m/s)

A Honda moving at 100 km/h is 80 km behind a Ford moving in the same direction at 60 km/h. How far does the Honda travel before it catches up with the Ford? (200 km)

A man drives one-third of the distance home at 25.00 mph. How fast must he drive the rest of the way in order to average 35.00 mph for the entire trip? (v = 43.75 mph)

A woman on a bicycle climbs a hill at 4.0 m/s and then returns down the same hill at 8.0 m/s. what is her averge speed for the entire trip? (avg v = 5.3 m/s not 6 m/s!)

26. For the following velocity graph, sketch the displacement graph. Describe the motion of the object

27. For the following velocity graph, sketch the displacement graph. Describe the motion of the object

28. For the following displacement graph, sketch the velocity graph. Describe the motion of the object

29. For the following displacement graph, sketch the velocity graph. Describe the motion of the object

  30. How did Galileo make the argument that all objects fall at the same rate if you neglect air resistance?

If the acceleration due to gravity is 9.8 m/s^2, and I throw an object up into the air, how much does the speed of that object change every second? (Specify also if it is speeding up or slowing down).

If an object is dropped straight down, how much does the speed of that object change every second? (Also indicate if it is speeding up or slowing down).

In class we established that an object falls three times farther from 1 to 2 seconds compared to the first second, and five times farther from 2 to 3 seconds compared to the first second. Verify that an object will drop seven times farther from 3 to 4 seconds, nine times farther from 4 to 5 seconds, and eleven times farther from 5 to 6 seconds as compared to the first second. Do this by finding how far it dropped in that particular second (not the overall distance, but just in that second), and divide by 4.9.

31. Make a logical argument for the following statement: An object will come back to your hand with the same speed with which it was thrown.

Given the last statment: why is not a good idea to shoot a gun straight into the air and stand right underneath and look up? (You could even say with a bow and arrow too).

Your free-fall distance vs. time graph shows a curve that is going up, which means the object is speeding up. Construct a graph for speed vs. time. This is not a sketch. Use the actual values for the x and y axis. Use 1, 2, 3,... seconds for the x-axis, which is time, and decide what the y-axis values should be.

Now make a graph of velocity vs. time with the actual values. This is not a sketch!

32. A man standing at the edge of a cliff drops a rock from rest. He counts 4.5 seconds before it hits the ground. How high is the cliff? (99.2 m)

A woman standing at the edge of a cliff drops a rock from rest. If the cliff is 122.5 meters tall, how long will it take the rock to hit the bottom? (5.0 s)

An apple is thrown vertically downward from a cliff 48 m high and reaches the ground 2.0 s later. What was the apple’s initial velocity? (The initial velocity is not zero this time)! (-14 m/s)

33. A woman throws a golf ball straight into the air at 58.8 m/s. What is the velocity of the ball after 5 seconds? (+ 9.8 m/s)

At what time would the ball be the same speed but opposite direction? Do this logically and using an equation to show you get the same answer. (7.0 s)

How long did it take the ball to reach its maximum height? (6.0 s)

How high did it go? (176.4 m)

Where is the ball after 8.0 seconds? (+ 156.8 m)

What overall distance did it travel in that 8.0 seconds? (196 m)

How long does it take for the ball to return to the woman's hand? Do this logically and using an equation(12 s)

Why are you able to answer levels 2 and 7 logically and without an equation?

34. A nerf dart is shot straight into the air and it takes 5.0 seconds to reach the top of its flight. What was its initial velocity? (+ 49 m/s)

A bank robber is standing on the edge of a bridge that spans over a highway, and is 20 meters in the air. If he wants to drop the bag of money into the bed of a truck that is traveling at 30 m/s, how far away should the truck be when he drops the bag? (x = 60.6 m)

The robber decides to throw the bag down instead of just dropping it. If he throws it with an initial velocity of -5.0 m/s, how far away should the truck be now? (x = 46.6 m)