ef- .. 17 The position of a particle moving along the x axis is given in centime

Question

ef- .. 17 The position of a particle moving along the x axis is given in centimeters byx = 9.75 + 1.50t, where t is in seconds. Calculate (a) the average velocity during the time interval t = 2.00s to t = 3.00 s; (b) the instantaneous velocity at t 2.00 s; (c) the instantaneous ve- locity at t = 3.00 s; (d) the instantaneous velocity at t = 2.50 s; and (e) the instantaneous velocity when the particle is midway between its positions at t = 2.00 s and t = 3.00 s. (f) Graph x versus t and in- r answers graphically.

Explanation / Answer

a) x(2) = 9.75 + 1.5(2)³ = 21.75

x(3) = 9.75 + 1.5(3)³ = 50.25

Vavg = x / t = (50.25 – 21.75) / 1s 28.5 cm/s

b) v(t) = dx(t)/dt = 4.5t², so

v(2) = 4.5(2)² = 18 cm/s

c) v(3) = 4.5(3)² = 40.5 cm/s

d) v(2.5) = 4.5(2.5)² = 28.125 cm/s

e) x = ½(21.75 + 50.25) = 36 = 9.75 + 1.5t³

t = 2.6 s

v(2.6) = 4.5(2.6)² = 30.33 cm/s

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