Suppose the position of an object moving horizontally after t seconds is given b

Question

Suppose the position of an object moving horizontally after t seconds is given by the following function s-f(t), where s is measured in feet, with s> 0 corresponding to positions right of the origin a. Graph the position function. b. Find and graph the velocity function. When is the object stationary, moving to the right, and moving to the left? C. Determine the velocity and acceleration of the object at t = 1 d. Determine the acceleration of the object when its velocity is zero. e. On what intervals is the speed increasing? f(t) = t3-15t2 + 72t; 0sts8 When is the object moving to the left? The object is moving to the left on the interval(s) (4,6) Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.) C. The velocity of the object at t = 1 is 45 ft / s. (Simplify your answer.) The acceleration of the object at t 1 is -24 ft/s2. (Simplify your answer.) The acceleration of the object at t = 1 is -24 ft/ s. (Simplify your answer.) d. The acceleration each time the velocity is zero is - 6,6 ft/s2. (Simplify your answer. Use a comma to separate answers as needed.) e. On what intervals is the speed increasing? 1 The speed is increasing on the interval(s). (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.)

Explanation / Answer

f(t)=t3-15t2+72t

velocity, f '(t)= 3t2-30t +72

3t2-30t+72 >0

t2-10t +24>0

(t-6)(t-4)>0

testing points

t-6=0 , t-4=0

t=6, 4

IN (0,4), we will get positive

In (4,6), we will get negative

In (6, infinity), we will get positive

So the required interval is (-infinity,4)U(6,infinity)

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