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R.R. Jha
R.R. Jha, Tutor
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Experience:  B.Tech
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Sketch a position vs time graph, a velocity vs time graph

Customer Question

Sketch a position vs time graph, a velocity vs time graph and an acceleration vs time graph for a bus traveling west and speeding up. If you cannot sketch it just describe it in detail that would be fine. For example you can say on the X axis is displacement and time on yaxis and the graph will be a line starting from 0,0 and going down (in south east direction) at a constant slope etc..
Submitted: 6 years ago.
Category: Homework
Expert:  R.R. Jha replied 6 years ago.
Hi there,

I'd assume time on x-axis and other variable on y-axis. Let the acceleration of the bus be 'α'. If the acceleration is constant, α is constant, and the equations for acceleration, velocity and displacement are

a = α (horizontal line cutting y axis at y=α)
v = u + αt (straight line with slope α, and cutting y-axis at y=u)
x = ut + ½ αt² (parabola)

Where u is the initial velocity of the bus at t=0.
Assuming u=1, α=1, the plots are as below
Acceleration

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Velocity

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Displacement

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Let me know if it needs more explanation.

Bonus is appreciated.
Have a good day !

Edited by RRJha on 9/28/2010 at 2:31 AM EST
Customer: replied 6 years ago.
Hi.. In the school (in the west) traveling west is graphed in the negative corodinates (up and East is positive) down and west is negative. Hence the graphs as shown above would not be correct. If you do not have exposure to this way of teaching then this may not a be a question you would like to attempt.
Expert:  R.R. Jha replied 6 years ago.
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Expert:  R.R. Jha replied 6 years ago.
Also note that, I've taken time on x-axis as before, which is the usual practice.
Customer: replied 6 years ago.
Just one question. Why is velocity not zero at time = zero (you start with value of one). Kindly clarify. You may be correct Just trying to understand. It is late here, unless you respond in next 5 minutes I will be able to view in my am. Thanks.
Expert:  R.R. Jha replied 6 years ago.
Since west is negative, velocity at t=0 is -1, and acceleration is -1.
At time t=0, when one starts to observer the bus, it might already be moving. If it just starts at t=0, velocity in that case would be 0.
Expert:  R.R. Jha replied 6 years ago.
Just a side note to help you with further graphs, first find the one variable as an algebraic function of another variable , then just draw graphs for that function.
Like,
Equations of motion are
v = u+at
d = ut + ½ at²

We assume u = -1, a = -1,
so
v = -1 - t (straight line with slope -1, and cutting vertical axis at v=-1)
d = -t - 0.5t² (parabola, in case you've encountered them, you'd soon)
Customer: replied 6 years ago.
I already accepted this a while ago but somehowthe system still shows this question unanswered. Hopefully this will help close this.

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