Question (part 1 of 3) Your A race car moves such that its position fits the rel

Question

Question (part 1 of 3) Your A race car moves such that its position fits the relationship z(t) (6 m/s)t+ (0.96 m/s3)3 where z is measured in meters and t in sec- onds. Approximate the instantaneous velocity at 3.1 s, using a centered time interval of 0.2 s. Answer in units of m/s Question (part 2 of 3) You Use a 0.4 s interval centered at 3.1 s to ap- proximate the instantaneous velocity at 3.1 s. Answer in units of m/s Question (part 3 of 3) You Find the average velocity during the 3.1 s. Answer in units of m/s.

Explanation / Answer

(part 1 of 3 )

x(t) = 6 t + (0.96) t3

taking derivative both side relative to "t"

dx(t)/dt = 6 + 3 (0.96) t2

v(t) = 6 + 2.88 t2

at t = 3.1 , instanteneous velocity is given as

v(3.1) = 6 + 2.88 (3.1)2

v(3.1) = 33.7 m/s

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