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Question

Suppose an arrow is shot upward on a certain planet with a velocity of 34 m/s, then its height in meters after  seconds is given by h(t)=34t−4.2t^2.

A) Find the average velocity between t=3.8 and  t=4.3 seconds.

B) Find the instantaneous velocity at t=3.8 seconds.

C) Find the acceleration at t=3.8 seconds

Answer 1

h(t) = 34t -4.2t^2

velocity = v(t) = h'(t) = 34 -8.4t

v(3.8)= 34-8.4(3.8) = -2.08 = instantaneous velocity at time t=3.8 seconds

v(4.3)= 34-8.4(4.3) = -2.12

average velocity = [v(4.3)+v(3.8)]/2 = -2.10 meters per second

acceleration = h"(t) = v'(t) = a(t) = -8.4 meters per second per second