A drone is traveling in the positive direction along the x axis and you have bee

Question

A drone is traveling in the positive direction along the x axis and you have been given the following information about its flight. It is at the position x - 0 at the time t 0, and its velocity along the x axis at any time is given by v(t) -b ct2, where b 20.3 m/s, c 11.5 m/s3, and v is in m/s when t is entered in seconds. Determine the following. (a) the time at which the drone changes direction (b) location of the drone when it changes direction (c) acceleration of the drone when it changes direction (Indicate the direction with the sign of your answer.)

Explanation / Answer

a] It is the time when v = 0,

b - ct^2 = 0

t = sqrt(b/c) = sqrt(20.3/11.5) = 1.3286 s

b] x = integral vdt = bt - ct^3/3 = 20.3*1.3286 - 11.5*1.3286^3/3

= 17.98 m

c] a = dv/dt = -2ct = -2*11.5*1.3286 = -30.6 m/s^2

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