# Velocity as a function of time

• Sep 18th 2009, 01:46 PM
BiGpO6790
Velocity as a function of time
Please explain how to interpret this graph as well as the rest of the problem. Thank you!

Two horizontal forces http://edugen.wiley.com/edugen/cours...ta/up/Fvec.gif1 and http://edugen.wiley.com/edugen/cours...ta/up/Fvec.gif2 act on a 3.0 kg disk that slides over frictionless ice, on which an xy coordinate system is laid out. Force http://edugen.wiley.com/edugen/cours...ta/up/Fvec.gif1 is in the positive direction of the x axis and has a magnitude of 6.7 N. Force http://edugen.wiley.com/edugen/cours...ta/up/Fvec.gif2 has a magnitude of 9.0 N. Figure 5-34 gives the x component vx of the velocity of the disk as a function of time t during the sliding. What is the angle between the constant directions of forces http://edugen.wiley.com/edugen/cours...ta/up/Fvec.gif1 and http://edugen.wiley.com/edugen/cours...ta/up/Fvec.gif2?
http://edugen.wiley.com/edugen/cours...5/fig05_34.gifFig. 5-34
Problem 12.
• Sep 22nd 2009, 04:53 PM
sethborders
This problem asks to to relate kinematics (motion) and dynamics (forces). This should instantly make you think Fnet=m*a. Mainily we are woried about the x component, though, so we'll say Fnet_x = m*a_x.

Now, you should know, that acceleration is a derivative of velocity, and that on a graph, the derivative is the slope. so a = dv/dx = rise/run = 6/2 = 3 m/s^2.

now, we have a mass of 3.0 kg, and an acceleration of 3m/s^2, so Fnet_x = 3*3 = 9N.

now, its a matter of adding the forces:
Fnet_x = F1_x + F2_x

F1 is along the X axis:
F1_x = F1 = 6.7N
F2 is not so we multiply its magnitude by cos(theta):
F2_x = F2*cos(th) = 9N*cos(th)