24. The velocity of an object as it moves along the x-axis obeys the function v(

Question

24. The velocity of an object as it moves along the x-axis obeys the function v(t)9 velocity is measured in units of meters per second and time t is in seco a) Given the above expression, state the numerical values of the object's initial Vci be nds. as its acceleration, including proper units. Describe also in words the motion o velocity as well the object b) Determine the object's velocity at t-4.00 s. At t-o, the initial position of the object is x,-5 m. Determine the expression for x(1) , and using this expression determine the object's position at t4.00 s. c) d) Does the object ever reverse its direction of movement? If so, determine the time t when this occurs, as well as the object's position at that instant e) Does the object ever return to its starting point? If so, determine the time t when this occurs, and the object's velocity (how fast and in what direction the object is moving).

Explanation / Answer

24. givne for 1 d motion along x axis

v(t) = 9 - 6t

v is in m/s, t is in s

a. givne v(t)

inittial velocity, vo = v(0) = 9 - 0 = 9 m/s

acceleration = v' = -6 m/s/s

b. at t= 4 s

v(4) = 9 - 36 = -27 m/s

c. at t = 0, xi = 5 m

hence

integrating velocity

x = xi + 9t - 3t^2

x(4) = 5 + 36 - 48 = -7 m

d. object reverses its direction ofg motion when v = 0

t = 9/6 = 1.5 s

e. when x = xi, object has returned to original point

9 = 3t

t = 3 s

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