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 = 7.75 + 2.00t 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

Mean value of velocity 1/(b-a)int[V(t)] from a to b since V(t) is the first derivative of position wrt to time, you can skip the calculus part and simply evaluate 1/(3-2)(2t^3+8) from 2 to 3 [54+8]-[16+8] 62-24=38cm/s for the rest x(t)=2t^3+8 x'(t)=6t^2=V(t) (b) V(2)=24cm/s (c) V(3)=54cm/s (d) V(2.5)=37.5 (e) x(t)=2t^3+8 x(2)=24 x(3)=62 (62-24)/2=19, 19+24=43 43=2t^3+8 35/2=t^3 V=6[(35/2)^1/3]^2~40.443cm/s

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