7. An object with an unknown initial velocity has a constant acceleration with components ax = 8 m/s? and a,= 0 . Which of the following is a possible expression for the position of this object, in meters, for both the x and y directions as functions of time? A. x = 8tandy = 0 B. x = 8t and y = 8t C. x = 80- and y = 8t2 V D. x = 412 and y =8t E. x = 402 and y = 4t2 8. A particle is moving along the y-axis. The particle's position as a function of time is given by y = at' - 8t + 4, where a = 1 m/s , 8 = 4 m/s, and = 3 m. What is the particle's acceleration at time t = 3.0 s? A. 6.0 m/s B. 9.0 m/s2 C. 15.0 m/s V D. 18.0 m/s E. 27.0 m/s 9. An object of mass 10 kg starts from rest at time *= 0 and moves in a straight line. For time t > 0, the object's velocity v as a function of time t is given by v = 2t + 3t , where v is in m/s and t is in seconds How far does the object travel during the first 10 s of its motion? A. 62 m B. 320 m C. 383 m V D. 1100 m E. 1600 m Page 21 of 22 equation x = 3.0t" + 1.5t + 4.5, where x is in meters and t is in seconds, What is the instantaneous acceleration of the object att = 3.0 s? A. 3.0 m/s V B. 6.0 m/s C. 9.0 m/s D. 19.5 m/s2 E. 36 m/s 11. The position x of an object is given as a function of time t by the equation x = 8 + 4t - 683, where x is in meters and t is in seconds. What is the maximum positive velocity attained by this object? V A. 4m/s B. 8m/s C. 18 m/s D. 36 m/s There is no maximum positive E. velocity because the object never moves in the positive direction. 12. A plane starts at rest on a straight runway. For the first 30 s, the plane's acceleration a is given as a function of time & by the equation a = Br, where B = 1/90 m/s* and t is in seconds. What is the plane's speed at t = 30 s ? A. 10 m/s B. 30 m/s V C. 100 m/s D. 150 m/s E. 300 m/s 13. The velocity v in meters per second of an object moving in a straight line is given as a function of time t in seconds by v = 4 + 2t. The total distance the object travels between t = 1 s and t = 2 s is A. 12 m B. 18m C. 24 m D. 30m E. 36 mWhich of the following statements must be true for a falling object that has been dropped from rest near the surface of Earth The derivative of the distance the A. object falls with respect to time equals 9.8 m/s The object falls a vertical distance of B. 9.8 m during the first second only. C. The object falls a vertical distance of 9.8 m during each second. D. The speed of the object as it falls is a constant 9.8 m/s. V E. The speed of the object increases by 9.8 m/s during each second. V. MOTION IN NON-UNIFORM ACCELERATION Question Proof/Work/Explanation 1. The speed v of an automobile moving on a straight road is given in meters per second as a function of time t in seconds by the following equation: v( t ) = 4 +25 What is the acceleration of the automobile at t = 2 s? A. 2 m/s B. 16 m/s2 C. 20 m/s2 V D. 24 m/s2 E. 28 m/s2 2. How far has the automobile traveled in the interval between t = 0 and t = 2 s? A. 16 m B. 20 m C. 24 m D. 32 m E. 72 m 3. A ball of mass 2.0 kg is thrown vertically upward from the top of a building. The ball's velocity v is given as a function of time t by the equation v(t) = 5 - 10t. The positive direction is upward. What is the ball's acceleration at time t = 1 s? V A. -10 m/s B. -5 m/s2 C. 0 D. 5 m/s2 E. 10 m/s2 4. If the ball reaches the ground at t = 2.0 s, what is the height of the building? A. 5m V B. 10 m C. 15 m D. 20 m 5. 30 m 5. At what time does the ball reach its maximum height above the building? A. 0.2 s 0.4 s V C. 0.5 s D. 1.0 s E. 2.0 s 6. The velocity of a particle moving along the x- axis is given as a function of time by the expression v(t) = 3.0t - 2.0t + 4.0, where v is in meters per second and t is in seconds. What is the acceleration of the particle at t = 2.0 s? A. 4.0 m/s2 B. 6.0 m/s2 C. 8.0 m/s2 V D. 10.0 m/s E. 12.0 m/s2