EXAMPLE 2.3 Catching a Fly Ball GOAL Apply the definition of instantaneous accel

Question

EXAMPLE 2.3 Catching a Fly Ball GOAL Apply the definition of instantaneous acceleration. v (m/s) u (m/s) PROBLEM A baseball player moves in a straight-line path in order to catch a fly ball hit to the outfield. His velocity as a function of time is shown in figure (a). Find his instantaneous acceleration at points 0,0, and C 0 23 4 0 23 4 STRATEGY At each point, the velocity vs. time graph is a straight line segment, so the instantaneous acceleration will be the slope of that segment. Select two points on each segment and use them to calculate the slope. SOLUTION Acceleration at Av 4.0 m/s 0 a +2.0 m/s? =-= = at 2.0 s-0 The acceleration at equals the slope of the line connecting the points (O s, O m/s) and (2.0 s, 4.0 m/s). Acceleration at Av 4.0 m/s - 4.0 m/s a=-= om/s2 = , 3.0 s-2.0 s Av = 0, because the segment is horizontal. Av 2.0 m/s 4.0 m/s , Acceleration at -=-2.0 m/s? 4.0 s-30s The acceleration at © equals the slope of the line connecting the points (3.0 s 4.0 m/s) and (4.0 s, 2.0 m/s).

Explanation / Answer

According to the concept of the motion in one dimensional

instantaneous acceleration =v2-v1/t2-t1

now we find the instantaneous acceleration of line A,B and C in figure b

instantaneous acceleration of line A=>a1=1-4/1-0=-3/1=- 3 m/s^2

instantaneous acceleration of line B=>a2=3-1/3-1=2/2=1 m/s^2

instantaneous acceleration if line C=>a3=3-3/5-3=0 m/s^2

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