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PHYSICS, M1 EQ-Bank 15

A table is slanted so a book resting on that table begins to accelerate at a constant value, \(a\).

If the book travels 45 cm in 1.0 seconds, determine its acceleration, \(a\)?   (2 marks)

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\(0.9\ \text{ms}^{-2}\ \ \text{down slope}\)

Show Worked Solution

\(u= 0\ \text{ms}^{-1}, \ t=1\ \text{s}, \ s = \dfrac{45}{100} = 0.45\ \text{m}\)

\(s\) \(=ut +\dfrac{1}{2}at^2\)  
\(0.45\) \(=0 + 0.5 \times a \times 1^2\)  
\(a\) \(=\dfrac{0.45}{0.5 \times 1^2}\)  
  \(=0.9\ \text{ms}^{-2}\ \ \text{down slope}\)  

PHYSICS, M1 EQ-Bank 14

Calculate the average acceleration of an airplane during landing if it touches down with a velocity of 60 m/s north and comes to a complete stop over a distance of 350 m.   (2 marks)

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\(5.14\ \text{ms}^{-2}\) to the south.

Show Worked Solution
\(v^2\) \(=u^2 +2as\)  
\(a\) \(=\dfrac{v^2-u^2}{2s}\)  
  \(=\dfrac{0-60^2}{2 \times 350}\)  
  \(=-5.14\ \text{ms}^{-2}\)  

 

  • The average acceleration of the airplane is 5.14 ms\(^{-2}\) to the south.

PHYSICS, M1 EQ-Bank 13

Outline an experimental procedure to determine the acceleration of a falling steel ball. Your explanation should include all the measurements that must be recorded, the calculations needed to compute the acceleration, and an identification of any potential sources of error in the experiment.   (6 marks)

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Procedure and Measurements:

  • Set up a vertical drop area with a height of two metres which can be measured using a measuring tape or ruler.
  • Position the steel ball at the measured height using a release mechanism or having someone drop it from the height of 2 metres from rest.
  • Start the stopwatch (or begin video recording) at the moment of release and stop the timer as soon as the ball hits the ground.
  • Repeat the drop several times (e.g., 3–5 trials) to obtain an average time of fall (\(t\)).
  • The acceleration of the ball can be calculated using the formula, \(s= ut + \dfrac{1}{2}at^2\), where \(u=0\ \text{ms}^{-1}\), \(s=2\ \text{m}\) and \(t\) is the time measured for the ball to drop. Rearranging the formula,  \(a= \dfrac{2s}{t^2}\).

Sources of Error:

  • Timing: Not starting the stopwatch at the exact times when the ball is released or stopping the stopwatch at the exact time when the ball hits the ground. 
  • Initial Velocity: if the person holding the steel ball does not drop it from rest.
  • Height: Inaccuracies in the measurement of the two metre drop height.
Show Worked Solution

Procedure and Measurements:

  • Set up a vertical drop area with a height of two metres which can be measured using a measuring tape or ruler.
  • Position the steel ball at the measured height using a release mechanism or having someone drop it from the height of 2 metres from rest.
  • Start the stopwatch (or begin video recording) at the moment of release and stop the timer as soon as the ball hits the ground.
  • Repeat the drop several times (e.g., 3–5 trials) to obtain an average time of fall (\(t\)).
  • The acceleration of the ball can be calculated using the formula, \(s= ut + \dfrac{1}{2}at^2\), where \(u=0\ \text{ms}^{-1}\), \(s=2\ \text{m}\) and \(t\) is the time measured for the ball to drop. Rearranging the formula,  \(a= \dfrac{2s}{t^2}\).

Sources of Error:

  • Timing: Not starting the stopwatch at the exact times when the ball is released or stopping the stopwatch at the exact time when the ball hits the ground. 
  • Initial Velocity: if the person holding the steel ball does not drop it from rest.
  • Height: Inaccuracies in the measurement of the two metre drop height.

PHYSICS, M1 EQ-Bank 2-3 MC

Using the velocity-time graph below
 

 
Part 1

Determine the magnitude of the displacement:

  1. \(32\ \text{m}\)
  2. \(40\ \text{m}\)
  3. \(48\ \text{m}\)
  4. \(64\ \text{m}\)

 
Part 2

Determine the average acceleration between 4 and 8 seconds:

  1. \(-4\ \text{ms}^{-2}\)
  2. \(-2\ \text{ms}^{-2}\)
  3. \(-1\ \text{ms}^{-2}\)
  4. \(2\ \text{ms}^{-2}\)
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Part 1: \(C\)

Part 2: \(B\)

Show Worked Solution

Part 1

  • The displacement for the motion can be calculated by finding the area under the velocity time graph. 
  • By splitting the graph up into the square and triangle, the area under the curve is:

\(\text{Area}\ =(4 \times 8) + (\dfrac{1}{2} \times 4 \times 8) = 32 +16 = 48\ \text{m}\)

\(\Rightarrow C\)
 

Part 2

  • Average acceleration between t=4 and t=8 is:

\(a= \dfrac{\Delta v}{\Delta t} = \dfrac{0-8}{8-4} = -2\ \text{ms}^{-2}\)

\(\Rightarrow B\)

PHYSICS, M1 EQ-Bank 1 MC

An airplane, initially moving at 15 m/s, accelerates for 12 seconds until it reaches a take-off speed of 75 m/s. What is its average acceleration?

  1. \(3\ \text{ms}^{-2}\)
  2. \(4\ \text{ms}^{-2}\)
  3. \(5\ \text{ms}^{-2}\)
  4. \(6\ \text{ms}^{-2}\)
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\(C\)

Show Worked Solution

Average acceleration:

\(\dfrac{\Delta v}{\Delta t} = \dfrac{75-15}{12} = 5\ \text{ms}^{-2}\)

\(\Rightarrow C\)

PHYSICS, M1 EQ-Bank 7

 A plane is travelling at 315 ms\(^{-1}\) north when it passes through a dense cloud and slows down to a velocity of 265 ms\(^{-1}\) for safety precautions.

The plane did not change direction and travelled 2.5 km while it was slowing down.

Using north as the positive direction for all calculations, determine:

  1. the change in velocity of the plane.   (1 mark)

  2. the plane's acceleration.   (2 marks)

  3. the time over which the plane slowed down.   (2 marks)

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a.   \(\text{50 ms}^{-1}\ \text{south}\)

b.   \(\text{5.8 ms}^{-2}\ \text{south}\) 

c.   \(\text{8.62 s}\)

Show Worked Solution
a.     \(\Delta v\) \(=v-u\)
    \(=265-315\)
    \(=-50\ \text{ms}^{-1}\)
    \(=50\ \text{ms}^{-1}\ \text{south}\)

 

b.    Using  \(v^2=u^2 +2as\)  (time is not given):

\(a\) \(=\dfrac{v^2-u^2}{2s}\)  
  \(=\dfrac{(265)^2-(315)^2}{2 \times 2500}\)  
  \(=-5.8\ \text{ms}^{-2}\)  
  \(=5.8\ \text{ms}^{-2}\) to the south.  

 

c.    Using  \(v=u+at\):

\(t\) \(=\dfrac{v-u}{a}\)  
  \(=\dfrac{265-315}{-5.8}\)  
  \(=8.62\ \text{s}\)  

PHYSICS, M1 EQ-Bank 4

A truck travelling in a straight line with a speed of 60 ms\(^{-1}\) slows down and comes to rest over a period of 20 seconds.

  1. Calculate the change in velocity of the truck.   (2 marks)

  2. Determine the average acceleration of the truck across the 20 seconds.   (2 marks)

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a.   \(-60\ \text{ms}^{-1}\)

b.   \(-3\ \text{ms}^{-2}\)

Show Worked Solution
a.     \(\Delta v\) \(=v-u\)
    \(=0-60\)
    \(=-60\ \text{ms}^{-1}\)

 

b.     \(a\) \(=\dfrac{v-u}{t}\)
    \(=\dfrac{-60}{20}\)
    \(=-3\ \text{ms}^{-2}\)

PHYSICS, M1 2013 HSC 22

This set of data was obtained from a motion investigation to determine the acceleration due to gravity on a planet other than Earth.
 

Time (s) Vertical velocity (m s\(^{-1}\))
0.60 0.02
1.00 0.09
1.20 0.12
1.40 0.17
1.80 0.23

 
Plot the data from the table, and then calculate the acceleration.  (3 marks)
 

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\(0.182\ \text{ms}^{-2}\)

Show Worked Solution

\(\text{Acceleration}\) \(=\dfrac{0.2-0.04}{1.6-0.72}\)  
  \(=\dfrac{0.16}{0.88}\)  
  \(=0.182\ \text{ms}^{-2}\)  

PHYSICS, M1 2012 HSC 21

  1. Outline a first-hand investigation that could be performed to measure a value for acceleration due to gravity.   (3 marks)

  2. How would you assess the accuracy of the result of the investigation?   (1 mark)

  3. How would you increase the reliability of the data collected?   (1 mark)

  4. How would you assess the reliability of the data collected?   (1 mark)

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a.    Timing of a falling mass.

  • Set up an electronic and automatic timing system with sensors to detect the presence of a small falling metal ball.
  • Heights for the ball should be set up between 0.2 m to 1 m with intervals every 0.2 m. To increase the reliability of the results, multiple trials should be conducted at each height and the average falling time for each height should be calculated which can then be used to graph the data.
  • The results should be plotted on a graph of height vs time\(^2\). This uses the equation  \(s=ut +\dfrac{1}{2}at^2\)  where  \(u=0\)  which becomes  \(s=\dfrac{1}{2}at^2\).
  • After plotting the data, the acceleration due to gravity, \(a\), can be calculated using  \(a=\dfrac{2s}{t^2}\), which will make it equal to 2 × the gradient of the line of best fit.

b.    Assessing accuracy of results:

  • Look up known value on a reliable website (e.g. National Measurement Institute).
  • Ensure the value is for the location of the experiment (it can differ slightly).
  • Compare the known value to the value determined experimentally and the closer they are, the greater the accuracy of the experiment.

c.    Increasing data reliability:

  • Conduct multiple trials at each height.
  • Use the average of the calculations as stated in the method above.

d.   Assessing data reliability:

  • Compare the values obtained at a single height.
  • If there is a large variation in the calculations conducted at the same height, the data collected is less reliable.

Show Worked Solution

a.    Timing of a falling mass.

  • Set up an electronic and automatic timing system with sensors to detect the presence of a small falling metal ball.
  • Heights for the ball should be set up between 0.2 m to 1 m with intervals every 0.2 m. To increase the reliability of the results, multiple trials should be conducted at each height and the average falling time for each height should be calculated which can then be used to graph the data.
  • The results should be plotted on a graph of height vs time\(^2\). This uses the equation  \(s=ut +\dfrac{1}{2}at^2\)  where  \(u=0\)  which becomes  \(s=\dfrac{1}{2}at^2\).
  • After plotting the data, the acceleration due to gravity, \(a\), can be calculated using  \(a=\dfrac{2s}{t^2}\), which will make it equal to 2 × the gradient of the line of best fit.
♦ Mean mark (a) 55%.

b.    Assessing accuracy of results:

  • Look up known value on a reliable website (e.g. National Measurement Institute).
  • Ensure the value is for the location of the experiment (it can differ slightly).
  • Compare the known value to the value determined experimentally and the closer they are, the greater the accuracy of the experiment.
♦♦♦ Mean mark (b) 26%.

c.    Increasing data reliability:

  • Conduct multiple trials at each height.
  • Use the average of the calculations as stated in the method above.

d.   Assessing data reliability:

  • Compare the values obtained at a single height.
  • If there is a large variation in the calculations conducted at the same height, the data collected is less reliable.
♦♦♦ Mean mark (d) 7%.