vy (m/s) F₁ (N) Force (200 Hz) Remote 1 2.0- t: 1.46707 s Fy: 0.009 N 1.5 Fy: 0.009 N 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0+ 0.0 * Rezero sensor Wheel Velocity (100 Hz) Remote 1 t: 1.46245 s 2.0- Vy: 0.223 m/s 1.5 Vy: 0.300 m/s 1.0 0.5 0.0 -0.5 -1.0 -1.5 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 -2.0- * ✔ 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Time (s) Wheel Acceleration (100 Hz) Remote 1 2.0 1.5 t: 1.46245 s ay: -0.261 m/s² ay: -0.218 m/s² ay (m/s²) 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0+ 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Time (s) 5.0 Time (s)

A motorboat cuts its engine when its speed is 10.0 m/s and then coasts to rest. The equation describing the motion of the motorboat during this period is = ie-a , where is tin? speed .at time t, , is the initial speed at t = 0, and r is a constant. At t = 20.0 s. the speed is 5.00 m/s. (a) Find the constant c. (b) What is the speed at t - 40.0 s? (c) Differentiate die expression for (l) and thus show that the acceleration of the boat is proportional to the speed at any time.

A student is asked to measure the acceleration of a glider on a frictionless, inclined plane, using an air track, a stopwatch, and a meterstick. The top of the track is measured to be 1.774 cm higher than the bottom of the track, and the length of the track is d = 127.1 cm. The cart is released from rest at the top of the incline, taken as x = 0, and its position along the incline is measured as a function of time. For x values of 10.0 cm, 20.0 cm, 35.0 cm, 50.0 cm, 75.0 cm, and 100 cm, the measured times at which these positions are reached (averaged over five runs) are 1.02 s, 1.53 s, 2.01 s, 2.64 s, 3.30 s, and 3.75 s, respectively, (a) Construct a graph of x versus t2, with a best-fit straight line to describe the data, (b) Determine the acceleration of the cart from the slope of this graph, (c) Explain how your answer to part (b) compares with the theoretical value you calculate using a = g sin as derived in Example 5.6.

A student at the top of a building of height h throws one ball upward with a speed of i and then throws a second ball downward with the same initial speed i. Just before it reaches the ground, is the final speed of the ball thrown upward (a) larger, (b) smaller, or (c) the same in magnitude, compared with the final speed of the ball thrown downward?

A ball starts from rest and accelerates at 0.5(H) m/s2 while moving down an inclined plane 9.00 m long. When it reaches the bottom, the ball rolls up another plane, where it comes to rest after moving 15.0 m on that plane. (a) What is the speed of the ball at the bottom of the first plane? (b) During what lime interval does the ball roll down the first plane? (c) What is the acceleration along the second plane? (d) What is the balls speed 8.00 m along the second plane?

A toy cannon uses a spring to project a 5.30-g soft rubber ball. The spring is originally compressed by 5.00 cm and has a force constant of 8.00 N/m. When the cannon is fired, the ball moves 15.0 cm through the horizontal barrel of the cannon, and the barrel exerts a constant friction force of 0.032 0 N on the ball. (a) With what speed does the projectile leave the barrel of the cannon? (b) At what point does the hall have maximum speed? (c) What is this maximum speed?

What is the speed of the bird in Exercise 2.4?

A hare and a tortoise compete in a race over a straight course 1.00 km long. The tortoise crawls at a speed of 0.200 m/s toward the finish line. The hare runs at a speed of 8.00 m/s toward the finish line for 0.800 km and then stops to tease the slow-moving tortoise as the tortoise eventually passes by. The hare waits for a while after the tortoise passes and then runs toward the finish line again at 8.00 m/s. Both the hare and the tortoise cross the finish line at the exact same instant. Assume both animals, when moving, move steadily at their respective speeds. (a) How far is the tortoise from the finish line when the hare resumes the race? (b) For how long in time was the hare stationary?

A student working on a school project modeled a trampoline as a spring obeying Hookes law and measured the spring constant of a certain trampoline as 4617 N/m. If a child of mass 27.0 kg compresses the trampoline vertically by a maximum of 0.25 m, while bouncing up and down, what is the childs acceleration at the moment of maximum compression?

A student is asked to measure the acceleration of a glider on a frictionless, inclined plane, using an air track, a stopwatch, and a meterstick. The top of the track is measured to be 1.774 cm higher than the bottom of the track, and the length of the track is d = 127.1 cm. The cart is released from rest at the top of the incline, taken as x = 0, and its position x along the incline is measured as a function of time. For x values of 10.0 cm, 20.0 cm, 35.0 cm, 50.0 cm, 75.0 cm, and 100 cm, the measured times at which these positions are reached (averaged over five runs) are 1.02 s, 1.53 s, 2.01 s, 2.64 s, 3.30 s, and 3.75 s, respectively. (a) Construct a graph of x versus t2, with a best-fit straight line to describe the data. (b) Determine the acceleration of the cart from the slope of this graph. (c) Explain how your answer to part (b) compares with the theoretical value you calculate using a = g sin as derived in Example 4.3.