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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 1

A ball is thrown vertically upwards from ground level, it gains 50 metres vertically and then falls back to the ground.

  1. Determine the initial velocity, in metres per second, that the ball was thrown. Give your answer correct to one decimal place.   (2 marks)

  2. Calculate the total time of flight of the ball, in seconds, giving your answer correct to two decimal places.   (2 marks)

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a.    \(u=31.3\ \text{ms}^{-1}\)

b.   \(6.39\ \text{s}\).

Show Worked Solution

a.    \(\text{At 50 m}\ \Rightarrow\ v=0\ \text{ms}^{-1}\)

\(v^2\) \(=u^2+2as\)  
\(0^2\) \(=u^2+2 \times -9.8 \times 50\)  
\(u^2\) \(=980\)  
\(u\) \(=31.3\ \text{ms}^{-1}\)  

 

b.   \(\text{Time to highest point}\ = \dfrac{1}{2}\ \text{time of flight} \)

\(v\) \(=u+at\)  
\(0\) \(=31.3-9.8t\)  
\(9.8t\) \(=31.3\)  
\(t\) \(=3.194\ \text{s}\)  

 

\(\text{Total time of flight}\ = 2\times 3.194 = 6.39\ \text{s (2 d.p.)}\)

PHYSICS, M1 2017 VCE 9*

A model car of mass 2.0 kg is propelled from rest by a rocket motor that applies a constant horizontal force of 4.0 N, as shown below. Assume that friction is negligible.
 

With the same rocket motor, the car accelerates from rest for 10 seconds.

Calculate the the final speed of the model car?   (2 marks)

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\(20\ \text{ms}^{-1}\)

Show Worked Solution

\(a=\dfrac{F}{m} = \dfrac{4.0}{2.0} = 2\ \text{ms}^{-2} \)

\(v\) \(=u+at\)  
  \(=0+2 \times 10\)  
  \(=20\ \text{ms}^{-1}\)