Mr. mole left his burrow that lies below the ground and started digging his way deeper into the ground, descending at a rate of 1.8 meters per minute. after 5 minutes, he was 13.5 meters below the ground. let a (t), denote mr. mole's altitude relative to the ground a (measured in meters) as a function of time t (measured in minutes). write a function.

Question

Mathematics

Melody

5 May, 04:53

Mr. mole left his burrow that lies below the ground and started digging his way deeper into the ground, descending at a rate of 1.8 meters per minute. after 5 minutes, he was 13.5 meters below the ground. let a (t), denote mr. mole's altitude relative to the ground a (measured in meters) as a function of time t (measured in minutes). write a function.

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Amelie Wolf · Answer 1

Mr Mole's speed is 1.3 meters / min

after 5 min he was 13.5meters. that means the speed is not constant, so the expression of the equation of Mole's motion is as follow:

a (t) = 1/2ct² + Vit + a (0)

a (0) is assumed as 0

Vi = initial speed = 1.3 meters/min

c the acceleration of the movement, c is the unknown value we must find

after 5 min he was 13.5meters

13.5=1/2 c x25+1.8x5, it implies c=0.36

Finally the equation is

a (t) = 0.18 t² + 1.8 t