26.) Compare and contrast velocity and acceleration.

How are they the same (three ways)
How are they different? (one way)
Define each by the slope of a particular graph.














































27.) Can your body sense constant velocity? constant acceleration? Explain.

Your body cannot sense constant velocity. For example, you cannot sense that the earth is turning nor can you sense that the earth is orbiting around the sun. And, if you are in a vehicle that is traveling with a constant velocity, you cannot sense that you are moving unless your eyes sense a change in position. However, your body can sense constant acceleration. For example, you can sense a car speeding up or slowing down or a plane taking off, because the organs inside your body have inertia and they tend to stay in their present state of motion when other parts of your body are changing their state of motion. This difference can be sensed by nerves throughout your body.














































28. a) Are you accelerating if you are traveling in a constant direction with constant speed?

If you are traveling in a constant direction with constant speed there are no changes in velocity, so you are not accelerating.

28. b) Are you accelerating if you are traveling in a constant direction with changing speed?

If you are traveling in a constant direction with changing speed there is a change in velocity, so you are accelerating.

28. c) Are you accelerating if you are traveling at a constant speed with changing direction?

If you are traveling at a constant speed with changing direction there is a change in velocity, so you are accelerating.














































29.) By how much does the speed of a vehicle moving in a straight line change each second when it is accelerating at 2 km per hour per second (km/h/s)? at 5 km/h/s? at 10 km/h/s ?

        2km/h ;         5km/h ;         10km/h














































30.) Explain the units of acceleration (m/s2) in words.

Acceleration is a measure of the change in velocity over time. The change in velocity is measured in meter per second (m/s), and time interval is measured in second (s). Therefore, acceleration measures the change in meters per second every second [(m/s)/s], namely meters per second per second OR meters per second squared (m/s2).














































31 a) If an object has zero acceleration, does that mean its velocity is zero? Explain.

If an object has zero acceleration, its velocity doesn’t have to be zero. Acceleration is a measure of the change in velocity over time. Zero acceleration means there is no change in velocity over time, namely constant velocity. Constant velocity can be any velocity (including zero velocity or "at rest"), so the object’s velocity doesn’t have to be zero to have zero acceleration.

31 b) If an object has zero velocity at some instant, does that mean its acceleration is zero? Explain.

If an object has zero velocity at some instant, its acceleration doesn’t have to be zero. Acceleration is a measure of the change in velocity over time. An object could be changing its direction and in doing so its velocity would instantaneously go to zero as it went from positive to negative or from negative to positive. If the velocity is changing it is accelerating. Therefore, it can be accelerating while its velocity is zero. An example would be a ball tied to an elastic. At first it is slowing down while traveling in the positive direction until it reaches zero velocity and then speeding up in the negative direction, all the while traveling with constant acceleration in the negative direction.














































32.) Can an object change its direction when its acceleration is constant? Explain.

What is acceleration a measure of?
Acceleration is constant if the object's velocity is changing at a constant rate.
Could the velocity be changing at a constant rate and go from positive to negative or negative to positive?
Does your answer to the previous question mean a change in direction?
Check out the example of the ball in
question 31b.














































33.) Why is it that an object can accelerate while traveling at constant speed, but not at constant velocity?

An object can accelerate while traveling at constant speed but not at constant velocity. This is because acceleration is a measure of the change in velocity over time. Speed is a scalar quantity with magnitude but not direction while velocity is a vector quantity with both magnitude and direction. Therefore, at a constant speed (meaning no change in the magnitude of the velocity) an object could be changing its direction, and thus, accelerating. On the other hand, a constant velocity means no change in velocity (both magnitude and direction), so in this case the acceleration must be zero (no acceleration).














































34.) Which of the following are examples of accelerated motion?
    a) a train moving on a straight track at constant speed.
    b) a train moving on a curved track at constant speed.
    c) a train moving on a straight track at varying speed.

The trains described in cases b & c are examples of accelerated motion because the train in case "b" is changing its direction and the train in case "c" is changing the magnitude of the velocity.














































35.) A NASA ground team oversees a space shuttle launch in Florida and then travels to California to supervise the landing. When they meet up again, will the astronauts or the ground team have experienced the greater average acceleration

A NASA ground team oversees a space shuttle launch in Florida and then travels to California to supervise the landing. When they meet up again, the astronauts and the ground team have experienced the same average acceleration. They have both the same starting position and the same ending position, so the astronauts and the ground team have the same change in position. They both start and end at the same time, so the change in time is the same for each group. Since acceleration is a measure of the change in velocity over time and velocity is a measure of the change in position over time, having the same change in position means they have the same average acceleration.














































36.) Which has the greater acceleration: a car that goes from 70 km/h to 100 km/h or a bike that goes from 5 km/h to 35 km/h in the same period of time?

The car and the bike have the same acceleration because they have the same change in velocity ( 30 km/h ) over the same period of time.














































37.) The "hill" people measure heights using the top of the highest peak as their reference point and down as the positive direction. "Valley" people use the river bottom as their reference point and up as the positive direction. If both groups observed a rock falling, would they agree on its acceleration?

The “hill” people and the “valley” people would agree on its speed and distance because both of these are scalar quantities. A scalar means they measure magnitude only. However, they would not agree on its velocity and displacement because both of these are vector quantities. Vector measurements include magnitude and direction. Since the two groups see direction in opposite ways, they would have values that were equal in magnitude but opposite in direction. Therefore, the “hill” people and the “valley” people would not agree on the rock’s acceleration because it is a vector quantity with both magnitude and direction and they have opposite ways of measuring the direction.














































38 a) Can you have positive velocity and negative acceleration at the same time? Explain.

38 b) Can you have negative velocity and positive acceleration at the same time? Explain.

What does a positive or a negative velocity tell you about the direction of the motion?
What happens to your velocity if you have acceleration in the same direction as your velocity?
What happens to your velocity if you have acceleration in the opposite direction to your velocity?














































39.) Describe a situation for each case in #13 above.

a) A ball slowing down as it moves uphill.
b) A braking force applied on a car while it is moving west.














































40.) Will your speed increase, decrease, or stay the same if you have:
      a) positive velocity and positive acceleration?      increase
      b) positive velocity and negative acceleration?     decrease
      c) positive velocity and zero acceleration?             stay the same
      d) negative velocity and positive acceleration?      decrease
      e) negative velocity and negative acceleration?     increase
      f) negative velocity and zero acceleration?             stay the same














































41.) On an acceleration-time graph, which is the dependent variable and which is the independent variable?

On a acceleration-time graph, acceleration is the dependent variable and time is the independent variable. Therefore, the acceleration will be on the y-axis and the time will be on the x-axis.














































42.) Sketch an acceleration-time graph of a person whose speed is increasing in the positive direction, then decreasing in the positive direction, then increasing in the negative direction, then decreasing in the negative direction. Draw all four sections as equal periods of time.

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43.) What does the slope of a velocity-time graph measure?

The slope of a velocity-time graph measure acceleration. Since slope is defined as the "rise" over "run", then the slope of a velocity-time graph will be the change in velocity divided by the change in time, which is acceleration.














































44.)Given an acceleration-time graph, how do you calculate velocity?

Given an acceleration-time graph, you can calculate velocity by determining the area under the "curve" during that time interval. The area of a rectangle is found by multiplying the length by the height. In this case, you will have acceleration in m/s2 (height of rectangle) multiplied by time in s (length of rectangle), so the result will be velocity measured in m/s.














































45.) What can you deduce about the acceleration of an object if its velocity-time graph is a straight line:
        a) parallel to and above the t-axis?     Zero acceleration
        b) parallel to and below the t-axis?     Zero acceleration

Any line parallel to the t-axis has no slope and since the slope of any velocity-time graph is equal to the acceleration, then in both cases above the acceleration is zero.














































46.) State the initial direction of motion of a bottle dropped from a helicopter if:
    a) the helicopter is motionless with respect to Earth's surface.     downward
    b) the helicopter is descending with respect to Earth's surface.     downward
    c) the helicopter is ascending with respect to Earth's surface.     upward














































47.) List the necessary steps to determine the instantaneous acceleration of an object that has a non-linear velocity-time graph.

1) Plot the points from the given table of values and draw a smooth 'curve of best fit'.
2) Locate the centre of curvature for the curve that contains the point in time you want to determine the instantaneous acceleration for.
3) Draw a radius from the centre of curvature to that point.
4) Draw a line perpendicular to the radius that passes through the said point.
5) Find the slope of the line drawn in step four. This is the instantaneous acceleration of the object at that point in time.














































48.) List the steps to create an acceleration-time graph given a velocity-time graph.

1) Show the calculation to find the slope of the first line segment on the velocity-time graph.
2) Determine the slope of the remaining line segments on the velocity-time graph.
3) Create a table of values containing time intervals and accelerations.
4) Choose appropriate scale for the graph.
5) Draw and label a graph. Plot and connect the points.














































49.) List the steps to create a velocity-time graph given an acceleration-time graph.

1) Show the calculation to find the change in velocity using the area under the "curve" method for the first time interval on the acceleration-time graph.
2) Calculate the final velocity for the first time interval by rearranging: Δv = vf - vi and using the initial velocity given.
3) Use the final velocity of the first time interval as the initial velocity for the second time interval.
4) Determine the final velocity of each time interval by repeating steps 1 - 3.
5) Create a table of values with time intervals, initial velocities and final velocities.
6) Draw and label a graph. Plot and connect the points.