(b) Determine the acceleration at t = 2.0 s. SOLUTION (Use the following as necessary: t and At.) Knowing that the initial velocity at any time t is v, xi (39 – 0.8t2) m/s, find the velocity at any later time t + At: m/s Find the change in velocity over the time interval At: Δν. m/s To find the acceleration at any time t, divide this expression by At and take the limit of the result as At approaches zero: Av a = lim At-0 m/s? Δε Substitute t = 2.0 s (Enter your answer in m/s. Indicate the direction with the sign of your answer.): m/s?

If we apply the above equations to the case of an object that does not change its direction of travel as it moves with constant acceleration, we find that the object: Undergoes a displacement Ax = x- x, . Note that displacement is a positive quantity if x > x, and a negative quantity if x < x,. Has average velocity v = (x - x )/t = (v + vo)/2. Note that velocity has the same sign as displacement. Travels distance d = |Ax| = |x – x,| . Note that distance is always a positive quantity. Has average speed d/t . Note that speed is always a positive quantity. Has constant acceleration a = (v – vo)/t . Acceleration may be positive or negative, depending on how velocity changes. - Xo For the case of an object that does change its direction of travel as it moves with constant acceleration, which of the quantities listed above are different? Question

A ball is thrown from an initial height of 4 feet with an initial upward velocity of 29 fus. The ball's height h (in feet) after t seconds is given by the following. h-4+291-167 Find all values of t for which the ball's height is 16 feet. Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.) initial height ground - seconds O-O

The position of a particle moving under uniform acceleration is some function of time t and the acceleration a. Suppose we write this position as x=ka™t", where k is a dimensionless constant. What values must m and n have? x = kamt"

solve the following exercise

A 2-stage rocket is fired from rest. Its acceleration data are shown in the graph below. Plot the v-t and s-t graphs describing the motion of the rocket-clearly showing the shape of the curve (or add a note) and values at inflection points. Show any calculations as well. Then find the velocity of the rocket and its elevation after 20 seconds of flight. a (m/s?) 25 18 (s) 15 20

A model rocket is launched with an initial upward velocity of 195 ft/s. The rocket's height h (in feet) after t seconds is given by the following. h=195t–16 Find all values of t for which the rocket's height is 87 feet. Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.) t = || seconds or O ground