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1.If the velocity of a particle is increasing at a constant rateits mean and instantaneous acceleration are the same.
2. Knowing the position and velocity of a particle allows itsfuture position to be predicted even if its acceleration isunknown.
3. For problems involving constant acceleration the mean andinstantaneous velocity are the same.
4. The slope of the displacement time graph is the instantaneousvelocity.
5. Instaneous velocity is the derivative of the displacement timefunction.

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Deanna Hettinger
Deanna HettingerLv2
29 May 2019
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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

 

to change the rate of their rotation with virtually constant angular acceleration. Many introductory problems in rotational kinematics involve the motion of a particle with constant, nonzero angular acceleration. The kinematic equations for such motion can be written as

\theta (t) = \theta_0 +\omega_0t + \frac{1}{2}\alpha t^2

and

\omega (t) = \omega_0 + \alpha t.

Here, the symbols are defined as follows:

  • theta(t) is the angular position of the particle at a time t.
  • theta_0 is the initial angular position of the particle.
  • omega(t) is the angular velocity of the particle at a time t.
  • omega_0 is the initial angular velocity of the particle.
  • alpha is the angular acceleration of the particle.
  • t is the time that has elapsed since the particle was located at its initial position.
In answering the following questions, assume that the angular acceleration is constant and nonzero: \alpha \neq 0.
 
A)
True or false: The quantity represented by theta is a function of time (i.e., is not constant).
 
  true
  false
   
B)
True or false: The quantity represented by theta_0 is a function of time (i.e., is not constant).
 
 
  true
  false
   
C)
True or false: The quantity represented by omega_0 is a function of time (i.e., is not constant).
 
 
  true
  false
   
D)
True or false: The quantity represented by omega is a function of time (i.e., is not constant).
 
 
  true
  false
   
E)
Which of the following equations is not an explicit function of time t? Keep in mind that an equation that is an explicit function of time involves t as a variable.
 
 
  \theta=\theta_0+\omega_0 t+\frac{1}{2}\alpha t^2
  \omega=\omega_0+\alpha t
  \omega^2=\omega_0^2+2\alpha(\theta-\theta_0)
   
F)
In the equation \omega=\omega_0+\alpha t, what does the time variable t represent?
Choose the answer that is always true. Several of the statements may be true in a particular problem, but only one is always true.
 
 
  the moment in time at which the angular velocity equals \omega_0
  the moment in time at which the angular velocity equals \omega
  the time elapsed from when the angular velocity equals \omega_0 until the angular velocity equals \omega
   
G)
Consider two particles A and B. The angular position of particle A, with constant angular acceleration, depends on time according to \theta_{\rm A}(t)=\theta_0+\omega_0t+\frac{_1}{^2}\alpha t^2. At time t=t_1, particle B, which also undergoes constant angular acceleration, has twice the angular acceleration, half the angular velocity, and the same angular position that particle A had at time t=0.
Which of the following equations describes the angular position of particle B?
 
  \theta_{\rm B}(t)=\theta_0+2\omega_0t+\frac{1}{4}\alpha t^2
  \theta_{\rm B}(t)=\theta_0+\frac{1}{2}\omega_0t+\alpha t^2
  \theta_{\rm B}(t)=\theta_0+2\omega_0(t-t_1) +\frac{1}{4}\alpha (t-t_1)^2
  \theta_{\rm B}(t)=\theta_0+\frac{1}{2}\omega_0(t-t_1)+\alpha (t-t_1)^2
  \theta_{\rm B}(t)=\theta_0+2\omega_0(t+t_1) +\frac{1}{4}\alpha (t+t_1)^2
  \theta_{\rm B}(t)=\theta_0+\frac{1}{2}\omega_0(t+t_1)+\alpha (t+t_1)^2
   
H)
How long after the time t_1 does the angular velocity of particle B equal that of particle A?
 
 
  \frac{\omega_0}{4\alpha}
  \frac{\omega_0+4\alpha t_1}{2\alpha}
  \frac{\omega_0+2\alpha t_1}{2\alpha}
  The two particles never have the same angular velocity.
   

1- Define velocity and acceleration in terms of position and time.differentiate between the instantaneous quantities and the averagequantities.

2- how are average velocity and instantaneous velocity related foran object moving at constant and non constant velocity?

3-how would you expect the graph of position versus time to lookfor a car moving at constant and non constant velocity on a track?explain how the graph would be?

4- what would a graph of instantaneous velocity versus time looklike for a car moving with constant velocity? or a car speeding up?or if the car is slowing down?

your help is much appreciated.

Rotational motion with a constant nonzero acceleration is not uncommon in the world around us. For instance, many machines have spinning parts. When the machine is turned on or off, the spinning parts tend to change the rate of their rotation with virtually constant angular acceleration. Many introductory problems in rotational kinematics involve the motion of a particle with constant, nonzero angular acceleration. The kinematic equations for such motion can be written as

\theta (t) = \theta_0 +\omega_0t + \frac{1}{2}\alpha t^2

and

\omega (t) = \omega_0 + \alpha t.

Here, the symbols are defined as follows:

  • theta(t) is the angular position of the particle at time t.
  • theta_0 is the initial angular position of the particle.
  • omega(t) is the angular velocity of the particle at time t.
  • omega_0 is the initial angular velocity of the particle.
  • alpha is the angular acceleration of the particle.
  • t is the time that has elapsed since the particle was located at its initial position.
In answering the following questions, assume that the angular acceleration is constant and nonzero: \alpha \neq 0.
 
A)
True or false: The quantity represented by theta is a function of time (i.e., is not constant).
 
  true
  false
   
B)
True or false: The quantity represented by theta_0 is a function of time (i.e., is not constant).
 
 
  true
  false
   
C)
True or false: The quantity represented by omega_0 is a function of time (i.e., is not constant).
 
 
  true
  false
   
D)
True or false: The quantity represented by omega is a function of time (i.e., is not constant).
 
 
  true
  false
   
E)
Which of the following equations is not an explicit function of time t? Keep in mind that an equation that is an explicit function of time involves t as a variable.
 
 
  \theta=\theta_0+\omega_0 t+\frac{1}{2}\alpha t^2
  \omega=\omega_0+\alpha t
  \omega^2=\omega_0^2+2\alpha(\theta-\theta_0)
   
F)
In the equation \omega=\omega_0+\alpha t, what does the time variable t represent?
Choose the answer that is always true. Several of the statements may be true in a particular problem, but only one is always true.
 
 
  the moment in time at which the angular velocity equals \omega_0
  the moment in time at which the angular velocity equals \omega
  the time elapsed from when the angular velocity equals \omega_0 until the angular velocity equals \omega
   
 

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