An object begins at position x = 0 and moves one-dimensionally along the x-axis with a velocity v expressed as a function of time t according to the graph above. At what time does the object pass through x = 0 again?   A: Between 10 s and 20 s B: Between 20 s and 30 s C: At 30 s exactly D: Between 30 s and 40 s E: After 40 s

In class, we used a numerical method to determine the velocity of an object at 0s and = t = 2.00 s given that the object had started from rest at t accelerated at a rate given by a(t) = (8.00 m/s^)t². Here's what we did: 1. Divided t into four intervals of 0.5 s each. 2. For each interval, calculated the average a. These were the numerical values we obtained for each time interval: 1 0.25 0.50 i t (s) a; (m/s²) After summing the values according to: 2 0.75 4.50 3 1.25 12.50 lim ã‚At, 2 V₂v₁ = limast. t₁ At→0 we arrived at the approximate value v = 21.0 m/s. 4 1.75 24.50 a (m/s²) 32.00+ 24.00 16.00 8.00 0 ā₁ 0 ā2 az as 0.50 1.00 1.50 2.00 t (s) 21.33 m/s. We then proceeded to integrate to obtain the analytical solution, which was v = Using the same numerical method, divide t into eight and then sixteen intervals to calculate the approximate value for v at t = 2.00 s. This should demonstrate that with more sampling, the AUC (area under the curve) value converges toward the analytical…

The Beretta Model 92S (the standard-issue U.S. army pistol) has a barrel 127 mmmm long. The bullets leave this barrel with a muzzle velocity of 349 m/sm/s. 1) What is the acceleration of the bullet while it is in the barrel, assuming it to be constant? Express your answer in meters per second squared. 2) What is the acceleration of the bullet while it is in the barrel, assuming it to be constant? Express your answer as a multiple of acceleration due to gravity g.   3) For how long is the bullet in the barrel? Express your answer in seconds.

At t=0 an object has a velocity of 35 m/s and a steady acceleration of -10 m/s2.   Make a sketch of velocity vs. time for this motion from t=0 to t=5 s. Make a sketch of acceleration vs. time for this motion from t=0 to t=5 s. Does the object change directions between 0 and 6 s?

Consider the following descriptions of the vertical motion of an object subject only to the acceleration due to gravity. Begin with the acceleration equation a(t) = v'(t) = g, where g= - 9.8 m/s. a. Find the velocity of the object for all relevant times. b. Find the position of the object for all relevant times. c. Find the time when the object reaches its highest point. What is the height? d. Find the time when the object strikes the ground. A softball is popped up vertically (from the ground) with a velocity of 25 m/s. а. v(t) b. s(t) = %3D c. The object's highest point is m at time t= S. (Simplify your answers. Round to two decimal places as needed.) d. t= (Simplify your answer. Round to two decimal places as needed.)

At t=0 an object has a position of 1 m and has a steady velocity of -2.5 m/s.     What will be the object’s position at t = 6 seconds? Make a sketch of position vs. time for this motion from t=0 to t=6 s. Make a sketch of velocity vs. time for this motion from t=0 to t=6 s. Does the object change directions between 0 and 6 s?