ECOR 1034 (ECOR1034) A/B/C Final Exam – Complete Solutions & Answers | Fall 2025–2026.

Carleton University: ECOR 1034 (ECOR1034) A/B/C Final Exam – Complete Solutions & Answers | Fall 2025–2026. ### 1. The same force (F) is applied to each cart and they move equal distances (d). In which one of these three cases is more work done by force (F)? A. Cart I B. Cart II C. Cart III D. The same work is done on each cart ### 2. The same force (F) is applied to each cart and they move equal distances (d). Which cart will have more kinetic energy at the end of distance (d)? A. Cart I B. Cart II C. Cart III D. All three will have the same kinetic energy ### 3. The same force (F) is applied to each cart and they move equal distances (d). Which cart will move faster at the end of distance (d)? A. Cart I B. Cart II C. Cart III D. All three will move with the same velocity ### 4. Approximately, what is the natural frequency of Cart III, if the spring has a stiffness of 100 N/m and (m = 1) kg? A. 0.53 Hz B. 0.92 rad/s C. 3.3 Hz D. 3.3 rad/s E. 5.7 rad/s ### 5. A particle strikes the smooth surface with a speed of 30 m/s. If (e = 0.8), (v_{x2}) is _____ after the collision. A. Zero B. Less than (v_{x1}) C. Greater than (v_{x1}) D. Equal to (v_{x1}) ### 6. A particle strikes the smooth surface with a speed of 30 m/s. If (e = 0.8), (v_{y2}) is _____ after the collision. A. 15 m/s B. 21 m/s C. 24 m/s D. 26 m/s ### 7. While the car, still pushing the truck, is speeding up to get up to cruising speed: A. The amount of force with which the car pushes on the truck is equal to that with which the truck pushes back on the car. B. The amount of force with which the car pushes on the truck is smaller than that with which the truck pushes back on the car. C. The amount of force with which the car pushes on the truck is greater than that with which the truck pushes back on the car. D. The car's engine is running so the car pushes against the truck, but the truck's engine is not running so the truck cannot push back against the car. The truck is pushed forward simply because it is in the way of the car. E. Neither the car nor the truck exert any force on the other. The truck is pushed forward simply because it is in the way of the car. ### 8. After the car reaches the constant cruising speed at which its driver wishes to push the truck: A. The amount of force with which the car pushes on the truck is equal to that with which the truck pushes back on the car. B. The amount of force with which the car pushes on the truck is smaller than that with which the truck pushes back on the car. C. The amount of force with which the car pushes on the truck is greater than that with which the truck pushes back on the car. D. The car's engine is running so the car pushes against the truck, but the truck's engine is not running so the truck cannot push back against the car. The truck is pushed forward simply because it is in the way of the car. E. Neither the car nor the truck exert any force on the other. The truck is pushed forward simply because it is in the way of the car. ### 9. A particle moves with acceleration (mathbf{a}=-kmathbf{v}), where (k) is a positive constant and (mathbf{v}) is velocity. What is the nature of its velocity over time? A. Constant B. Exponentially decreasing C. Linearly decreasing D. Oscillatory E. Inversely proportional ### 10. Which of the paths below would the puck most closely follow after receiving the kick? A. Path A — straight vertically upward B. Path B — straight diagonally upward and to the right C. Path C — initially upward, then curving to the right D. Path D — initially to the right, then curving upward E. Path E — curved/diagonal path upward and to the right ### 11. The speed of the puck just after it receives the kick is: A. Equal to the speed (v_o) it had before it received the kick. B. Equal to the speed (v_k) resulting from the kick and independent of the speed (v_o). C. Equal to the arithmetic sum of the speeds (v_o) and (v_k). D. Smaller than either of the speeds (v_o) or (v_k). E. Greater than either of the speeds (v_o) or (v_k), but less than the arithmetic sum of these two speeds. ### 12. Along the frictionless path you have chosen above, the speed of the puck after receiving the kick: A. Is constant. B. Continuously increases. C. Continuously decreases. D. Increases for a while and decreases thereafter. E. Is constant for a while and decreases thereafter. ### 13. Along the frictionless path you have chosen above, the main force(s) acting on the puck after receiving the kick is (are): A. A downward force of gravity. B. A downward force of gravity, and a horizontal force in the direction of motion. C. A downward force of gravity, an upward force exerted by the surface, and a horizontal force in the direction of motion. D. A downward force of gravity and an upward force exerted by the surface. E. None. (No forces act on the puck.) ### 14. A particle moves in a curve where the radius of curvature decreases as it speeds up. Which statement is correct? A. The normal acceleration depends only on speed, not curvature. B. The normal acceleration increases even if speed is constant. C. The tangential acceleration becomes zero when curvature changes. D. The normal acceleration becomes zero whenever the radius of curvature decreases. E. A decrease in curvature automatically increases the tangential acceleration. ### 15. A projectile is thrown with initial velocity (v_0), in a direction that makes an angle (theta) with the horizontal. Find the radius of curvature of the parabolic trajectory at the initial instant. A. (dfrac{v_0^2tantheta}{g}) B. (dfrac{v_0^2sintheta}{g}) C. (dfrac{v_0^2costheta}{g}) D. (dfrac{v_0^2}{gsintheta}) E. (dfrac{v_0^2}{gcostheta}) ### 16. An Impulsive Force (as defined in the Impulse–Momentum Principle) is characterized by: A. A force whose value changes smoothly with position. B. A force that does not change the particle's momentum. C. A small force acting over a long period of time. D. A large force acting over a very short period of time, causing a significant change in momentum. E. A constant force acting continuously throughout the entire motion of the particle. ### 17. A particle travels along the path (y=dfrac{x^3}{6}) m. When the particle reaches the point where (x=1) m, its speed is 3 m/s and its speed is increasing at a rate of 2 m/s². What is the magnitude of the particle's total acceleration vector at this point? A. 5.74 m/s² B. 8.14 m/s² C. 6.74 m/s² D. 7.24 m/s² E. 2.25 m/s² ### 18. A particle moves such that its velocity is zero, but acceleration is non-zero. Which statement is true? A. The particle is at rest permanently B. The particle changes direction C. The particle is moving at constant speed D. The particle is accelerating forward E. The particle is in free fall ### 19. Two projectiles are launched from the same location on level ground with the same initial speed (v_0). Projectile A is launched at angle (theta_A=20^circ) and Projectile B at (theta_B=70^circ). Neglecting air resistance, which statement is TRUE regarding their motion? A. Projectile A reaches a higher maximum height. B. Projectile B has a shorter total flight time. C. The velocity magnitude of both projectiles is zero at the maximum height. D. The two projectiles have the same horizontal range. E. Projectile B lands with a lower impact speed than Projectile A. ### 20. Figure 5 shows a boy swinging on a rope, starting at a point higher than A. Consider the following distinct forces: 1. A downward force of gravity. 2. A force exerted by the rope pointing from A to O. 3. A force in the direction of the boy’s motion. 4. A force pointing from O to A. Which of the above forces is (are) acting on the boy when he is at position A? A. 1 only B. 1 and 2 C. 1 and 3 D. 1, 2, and 3 E. 1, 3, and 4