By Paul Allen Tipler; Gene Mosca
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Extra resources for Physics for scientists and engineers [SOLUTIONS]
The average velocity is defined (for any acceleration) as the change in position (the displacement) divided by the change in time vav = ∆x ∆t . It is always valid. If the acceleration remains constant the average velocity is also given by vav = vi + vf 2 Consider an engine piston moving up and down as an example of non-constant velocity. For one complete cycle, vf = vi and xi = xf so vav = ∆x/∆t is zero. The formula involving the mean of vf and vi cannot be applied because the acceleration is not constant, and yields an incorrect nonzero value of vi.
Define the direction of your trip as the negative direction. During the last five steps gradually slow the speed of walking, until the wall is reached. 5 -1 v (m/s) -2 -3 -4 -5 t (s) 6 • Determine the Concept True. We can use the definition of average velocity to express the displacement ∆x as ∆x = vav∆t. Note that, if the acceleration is constant, the average velocity is also given by vav = (vi + vf)/2. 7 • Determine the Concept Acceleration is the slope of the velocity versus time curve, a = dv/dt; while velocity is the slope of the position versus time curve, v = dx/dt.
72 • Picture the Problem Because the acceleration of the object is constant we can use constant-acceleration equations to describe its motion. 0 m *73 • Picture the Problem Because the acceleration of the object is constant we can use constant-acceleration equations to describe its motion. 6 m s 2 2(4 m ) 74 • Picture the Problem Because the acceleration of the object is constant we can use constant-acceleration equations to describe its motion. 500 s aav 4 m s2 75 •• Picture the Problem In the absence of air resistance, the ball experiences constant acceleration.