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Mr.A.Gibson
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I'm ok with this question up until a3, I have no idea how to get velocity as a function of time from the information available. This question is taken from the Oxford Physics entrance exam. I'm not sure if it's a miss-print, perhaps the questions should be as a function of x, because that seems a lot easier and a similar level to questions from other years. Or perhaps I'm missing something.
22. A point like object with mass m = 1 kg starts from rest at point x0 = 10 m and moves without any friction under a force F which depends on the coordinate x as illustrated in figure below. The motion is confined to one dimension along x.
http://theonlinephysicstutor.com/Blog/Entries/2012/7/12_Entry_1_files/shapeimage_2.png

a1 What is its speed at x=0? [2]
a2 Sketch its kinetic energy as a function of x. [4]
a3 Sketch its velocity as well as its acceleration as a function of time t. [6]
Now consider a case when, in addition, a friction force of a magnitude of 1 N is present for x ≥ 0.
b1 Sketch how the velocity depends on x in that case. [6]
b2 How many meters this point like object traveled during the time when its position coordinate x was ≥ 0? [2]
22. A point like object with mass m = 1 kg starts from rest at point x0 = 10 m and moves without any friction under a force F which depends on the coordinate x as illustrated in figure below. The motion is confined to one dimension along x.
http://theonlinephysicstutor.com/Blog/Entries/2012/7/12_Entry_1_files/shapeimage_2.png

a1 What is its speed at x=0? [2]
a2 Sketch its kinetic energy as a function of x. [4]
a3 Sketch its velocity as well as its acceleration as a function of time t. [6]
Now consider a case when, in addition, a friction force of a magnitude of 1 N is present for x ≥ 0.
b1 Sketch how the velocity depends on x in that case. [6]
b2 How many meters this point like object traveled during the time when its position coordinate x was ≥ 0? [2]
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