The position of a particle moving along the x axis is given in centimeters by x

Question

The position of a particle moving along the x axis is given in centimeters by x = 9.75 + 3.50t 3, where t is in seconds. Consider the time interval t = 2.00 s to t = 3.00 s.

(a) Calculate the average velocity.
___cm/s

(b) Calculate the instantaneous velocity at t = 2.00 s.
___ cm/s

(c) Calculate the instantaneous velocity at t = 3.00 s.
___cm/s

(d) Calculate the instantaneous velocity at t = 2.50 s.
___cm/s

(e) Calculate the instantaneous velocity when the particle is midway between its positions at t = 2.00 s and t = 3.00 s.
___cm/s

Explanation / Answer

x = 9.75 + 3.50 t^3 Vave = (x 3 - x 2)/(3s-2s) = (104.25-37.75)m/2s = 66.5 m/s (b) take derivative to find instantaneous velocity 10.5 t^2 at 2.00s = 42m/s (c) same formula, now with t = 3.00 = 94.5 m/s (d) same formula, now with t = 2.50 = 65.625 m/s e) (104.25 + 37.75)/2 = 71m what time is it here 71 = 9.75 + 3.5t^3 t = CUBEROOT{(71-9.75)/3.5} = 2.596 use this in our derivative 10.5 t^2 with t = 2.596s = 70.8 m/s

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