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- Let s(t)= 8t^3−24t^2−192t be the equation of motion for a particle. Find a function for the velocity.v(t)= (ans) Where does the velocity equal zero? [Hint: factor out the GCF.]t= (ans) and t= (ans) Find a function for the acceleration of the particle.a(t)= (ans)Find f. + 2x + 8, f(1) = 2, f'(1) = -2 f(x) :Find y' and y'' for 2x3-5y2=8
- The position function of a spaceship is r(t) = (6 + t) i + (4 + ln(t)) j + (9-4/(t^2-1) k and the coordinates of a space station are (9, 6, 11). The captain wants the spaceship to coast into the space station. When should the engines be turned off? t=?Differentiate the function. 6x2 + 4x + 8 y = Vx y' =dy using implicit differentiation. dx Find
- Find the first and second derivative if w = 3z-2-(1/z)The position of a particle is given by the equation s(t)=10t^2−20 /3 t^3−5/4 t^4+t^5 where t is measured in seconds and s in meters. a. Find v(t). b. Find a(t). c. When is the particle at rest? d. When is the particle moving forward? e. When is the particle moving backward? f. Draw a diagram to represent the motion of the particle. g. Find the total distance traveled by the particle during the first four seconds.Find the derivative of the algebraic function H(v) = (v5 − 3)(v+ + 3). Select one: a. H'(v) = 9v³ +15v+ +12v³ b. H'(v) = 98 +12v4 - 3v³ c. H'(v) = 9v³ +15v+-12v³ H'(v)=9v8-15v4 -12v³ x d. e. H'(v) = 9v³ +12v++15v³ Incorrect