30 multiple-choice + 2 free-response = 32 questions · scalars & vectors · technical drawings · 1-D motion · motion graphs · projectiles
Which of these is a vector quantity?
C) 15 m/s west. Only 15 m/s west states a direction. Time, mass and temperature are scalars.
Answer: C) 15 m/s west. Only 15 m/s west states a direction. Time, mass and temperature are scalars.
Which list contains only scalar quantities?
D) Speed, time, mass. Speed, time and mass have size only. Each other list includes a vector: displacement, velocity/force, or acceleration.
Answer: D) Speed, time, mass. Speed, time and mass have size only. Each other list includes a vector: displacement, velocity/force, or acceleration.
A velociraptor runs 40 m east, then 40 m back west to its starting spot. What are its distance and displacement?
D) 80 m and 0 m. Distance is the total path: 40 + 40 = 80 m. Displacement is final minus start position. It ends where it began, so displacement = 0 m.
Answer: D) 80 m and 0 m. Distance is the total path: 40 + 40 = 80 m. Displacement is final minus start position. It ends where it began, so displacement = 0 m.
Your favorite PhysEng teacher jogs once around a 400 m track in 200 s, finishing at the start line. What are the average speed and average velocity?
B) 2 m/s and 0 m/s. Average speed = 400 m ÷ 200 s = 2 m/s. The displacement is 0 (back at the start), so average velocity = 0 ÷ 200 = 0 m/s.
Answer: B) 2 m/s and 0 m/s. Average speed = 400 m ÷ 200 s = 2 m/s. The displacement is 0 (back at the start), so average velocity = 0 ÷ 200 = 0 m/s.
(Vectors) A velociraptor moves 24 m north and 7 m east. What is the magnitude of its resultant displacement?
C) 25 m. R = √(24² + 7²) = √(576 + 49) = √625 = 25 m. 31 m (just adding) and 17 m (subtracting) are traps.
Answer: C) 25 m. R = √(24² + 7²) = √(576 + 49) = √625 = 25 m. 31 m (just adding) and 17 m (subtracting) are traps.
(Vectors) For the same raptor (24 m north, 7 m east), what is the direction of the resultant, measured counter-clockwise from east?
B) 73.7°. φ = tan⁻¹(24/7) = 73.7°. North and east are both +, so the resultant is in Q1 and θ = φ = 73.7°. (16.3° = tan⁻¹(7/24) uses the wrong ratio.)
Answer: B) 73.7°. φ = tan⁻¹(24/7) = 73.7°. North and east are both +, so the resultant is in Q1 and θ = φ = 73.7°. (16.3° = tan⁻¹(7/24) uses the wrong ratio.)
(Vectors) Your favorite PhysEng teacher runs 15 m west and 20 m south. What is the magnitude and direction of the resultant?
C) 25 m at 233°. R = √(15² + 20²) = 25 m. φ = tan⁻¹(20/15) = 53.1°. West and south are both −, which is Q3, so θ = 180° + 53.1° = 233.1° ≈ 233°.
Answer: C) 25 m at 233°. R = √(15² + 20²) = 25 m. φ = tan⁻¹(20/15) = 53.1°. West and south are both −, which is Q3, so θ = 180° + 53.1° = 233.1° ≈ 233°.
(Vectors) A raptor moves 8 m north and 6 m west. What is its resultant?
A) 10 m at 126.9°. R = √(8² + 6²) = 10 m. φ = tan⁻¹(8/6) = 53.1°. North (+) and west (−) put it in Q2, so θ = 180° − 53.1° = 126.9°.
Answer: A) 10 m at 126.9°. R = √(8² + 6²) = 10 m. φ = tan⁻¹(8/6) = 53.1°. North (+) and west (−) put it in Q2, so θ = 180° − 53.1° = 126.9°.
(Vectors) A velocity of 30 m/s points at 60° (counter-clockwise from east). What are its x- and y-components?
B) vx = 15.0 m/s, vy = 26.0 m/s. vx = 30 cos 60° = 30 × 0.5 = 15.0 m/s. vy = 30 sin 60° = 30 × 0.866 = 26.0 m/s. Swapping sin and cos gives the first option.
Answer: B) vx = 15.0 m/s, vy = 26.0 m/s. vx = 30 cos 60° = 30 × 0.5 = 15.0 m/s. vy = 30 sin 60° = 30 × 0.866 = 26.0 m/s. Swapping sin and cos gives the first option.
Which type of pictorial drawing has its three axes spaced 120° apart, with receding lines at 30° to the horizontal?
C) Isometric. Isometric means 'equal measure'. The three axes are 120° apart and receding edges are drawn at 30°.
Answer: C) Isometric. Isometric means 'equal measure'. The three axes are 120° apart and receding edges are drawn at 30°.
In which type of drawing do parallel depth lines converge toward a vanishing point?
A) Perspective. Perspective drawings converge to one or more vanishing points, like a photo. AutoCAD is software, not a drawing type.
Answer: A) Perspective. Perspective drawings converge to one or more vanishing points, like a photo. AutoCAD is software, not a drawing type.
Which drawing shows the front of an object in its true shape and size, with the depth lines drawn back at an angle (often 45°)?
B) Oblique. Oblique: the front face (the frontal lines) keeps true proportions, and depth recedes at an angle.
Answer: B) Oblique. Oblique: the front face (the frontal lines) keeps true proportions, and depth recedes at an angle.
A drawing shows an object as separate flat front, top and right-side views. What type of drawing is this?
D) Orthographic (multiview). Orthographic (multiview) projection shows each face as its own 2D view in true size and shape.
Answer: D) Orthographic (multiview). Orthographic (multiview) projection shows each face as its own 2D view in true size and shape.
A steel plate measures 5 cm by 9 cm. Scale it onto paper using the scale factor 3:1. What are the drawing's dimensions?
C) 15 cm by 27 cm. 3:1 means drawing : actual = 3 : 1, so every length is multiplied by 3: 5 × 3 = 15 cm and 9 × 3 = 27 cm. Adding 3 or dividing by 3 are traps.
Answer: C) 15 cm by 27 cm. 3:1 means drawing : actual = 3 : 1, so every length is multiplied by 3: 5 × 3 = 15 cm and 9 × 3 = 27 cm. Adding 3 or dividing by 3 are traps.
A 12 m long school bus is drawn at a scale of 1:100. How long is the bus on the drawing?
B) 12 cm. 12 m = 1200 cm. Drawing = 1200 ÷ 100 = 12 cm.
Answer: B) 12 cm. 12 m = 1200 cm. Drawing = 1200 ÷ 100 = 12 cm.
(1-D Motion) Your favorite PhysEng teacher is 120 m from the exit and runs at a constant velocity that gets them there in 15 s. What is the teacher's velocity?
D) 8.0 m/s. v = displacement ÷ time = 120 ÷ 15 = 8.0 m/s. 0.125 is time ÷ distance (upside down), and 9.81 is g, which is irrelevant here.
Answer: D) 8.0 m/s. v = displacement ÷ time = 120 ÷ 15 = 8.0 m/s. 0.125 is time ÷ distance (upside down), and 9.81 is g, which is irrelevant here.
(1-D Motion) A velociraptor accelerates uniformly from rest to 18 m/s in 3.0 s. What is its acceleration?
A) 6.0 m/s². a = (v − u) ÷ t = (18 − 0) ÷ 3.0 = 6.0 m/s².
Answer: A) 6.0 m/s². a = (v − u) ÷ t = (18 − 0) ÷ 3.0 = 6.0 m/s².
(1-D Motion) How far does that raptor travel during those 3.0 s?
D) 27 m. s = ut + ½at² = 0 + ½ × 6.0 × 3.0² = 27 m. As a check, average velocity (0 + 18)/2 = 9 m/s × 3 s = 27 m.
Answer: D) 27 m. s = ut + ½at² = 0 + ½ × 6.0 × 3.0² = 27 m. As a check, average velocity (0 + 18)/2 = 9 m/s × 3 s = 27 m.
(1-D Motion) A car moving at 30 m/s brakes with a constant acceleration of −6.0 m/s². How far does it travel before stopping?
A) 75 m. v² = u² + 2as → 0 = 30² + 2(−6.0)s → s = 900 ÷ 12 = 75 m.
Answer: A) 75 m. v² = u² + 2as → 0 = 30² + 2(−6.0)s → s = 900 ÷ 12 = 75 m.
(Free Fall) A textbook is dropped from rest off a 30 m high roof. How long does it take to hit the ground? (g = 9.81 m/s²)
C) 2.47 s. h = ½gt² → t = √(2h/g) = √(60 ÷ 9.81) = √6.12 = 2.47 s. The distractors forget the 2 or the square root.
Answer: C) 2.47 s. h = ½gt² → t = √(2h/g) = √(60 ÷ 9.81) = √6.12 = 2.47 s. The distractors forget the 2 or the square root.
(Graphing) What does the slope of a velocity–time graph represent?
B) Acceleration. Slope = Δv ÷ Δt, which is the definition of acceleration. The area under a v–t graph is displacement.
Answer: B) Acceleration. Slope = Δv ÷ Δt, which is the definition of acceleration. The area under a v–t graph is displacement.
(Graphing) The position–time graph shows a velociraptor moving in a straight line. What is its velocity?
A) 5.0 m/s. Slope of the x–t graph = rise ÷ run = 60 m ÷ 12 s = 5.0 m/s. The line is straight, so the velocity is constant.
Answer: A) 5.0 m/s. Slope of the x–t graph = rise ÷ run = 60 m ÷ 12 s = 5.0 m/s. The line is straight, so the velocity is constant.
(Graphing) The velocity–time graph shows your teacher's scooter. What is its acceleration?
C) 4.0 m/s². Slope of the v–t graph = Δv ÷ Δt = 20 ÷ 5 = 4.0 m/s².
Answer: C) 4.0 m/s². Slope of the v–t graph = Δv ÷ Δt = 20 ÷ 5 = 4.0 m/s².
(Graphing) Using the same velocity–time graph, how far does the scooter travel in the first 5 s?
D) 50 m. Displacement = area under the v–t graph. It is a triangle: ½ × 5 s × 20 m/s = 50 m. Using the rectangle (5 × 20) gives the 100 m trap.
Answer: D) 50 m. Displacement = area under the v–t graph. It is a triangle: ½ × 5 s × 20 m/s = 50 m. Using the rectangle (5 × 20) gives the 100 m trap.
(Graphing) On a velocity–time graph, a horizontal line above the time axis means the object is…
B) moving with constant velocity. A flat v–t line means v is not changing: constant velocity, zero acceleration. At rest would be a line on the time axis (v = 0).
Answer: B) moving with constant velocity. A flat v–t line means v is not changing: constant velocity, zero acceleration. At rest would be a line on the time axis (v = 0).
(Projectiles) A ball rolls horizontally off a 1.8 m high table at 4.0 m/s. How long is it in the air?
B) 0.61 s. Only the vertical motion sets the time: t = √(2h/g) = √(3.6 ÷ 9.81) = √0.367 = 0.61 s. The 4.0 m/s doesn't matter for the time.
Answer: B) 0.61 s. Only the vertical motion sets the time: t = √(2h/g) = √(3.6 ÷ 9.81) = √0.367 = 0.61 s. The 4.0 m/s doesn't matter for the time.
(Projectiles) How far from the base of the table does that ball land?
A) 2.4 m. Horizontal velocity is constant: x = vx × t = 4.0 × 0.606 = 2.4 m.
Answer: A) 2.4 m. Horizontal velocity is constant: x = vx × t = 4.0 × 0.606 = 2.4 m.
(Free Fall Extension) The fire department sets an inflatable cushion 5.0 m from the edge of an 11 m tall building. How fast must your favorite teacher be moving horizontally when leaping from the roof?
D) 3.3 m/s. Fall time: t = √(2 × 11 ÷ 9.81) = √2.24 = 1.50 s. Horizontal speed: v = 5.0 ÷ 1.50 = 3.3 m/s. It does matter: too slow and the teacher lands short.
Answer: D) 3.3 m/s. Fall time: t = √(2 × 11 ÷ 9.81) = √2.24 = 1.50 s. Horizontal speed: v = 5.0 ÷ 1.50 = 3.3 m/s. It does matter: too slow and the teacher lands short.
(Projectiles) A plane flying horizontally at 60 m/s drops a package. Ignoring air resistance, where is the package when it hits the ground?
D) Directly below the plane. The package keeps the plane's 60 m/s horizontal velocity (no horizontal force), so it stays directly under the plane the whole way down.
Answer: D) Directly below the plane. The package keeps the plane's 60 m/s horizontal velocity (no horizontal force), so it stays directly under the plane the whole way down.
(Projectiles) A ball is kicked at an angle above level ground. At the very top of its path, which is true?
C) Its vertical velocity is zero; its horizontal velocity is unchanged. At the peak vy = 0 (it stops rising). vx never changes, and acceleration is still g = 9.81 m/s² downward the whole time.
Answer: C) Its vertical velocity is zero; its horizontal velocity is unchanged. At the peak vy = 0 (it stops rising). vx never changes, and acceleration is still g = 9.81 m/s² downward the whole time.
A toy car rolls horizontally off a 0.95 m high shelf at 2.6 m/s. (a) How long is it in the air? (b) How far from the shelf does it land? (c) What is its vertical velocity just before impact? Give the magnitude and direction. (d) What is the magnitude of its total velocity just before impact?
At the same instant and from the same height, Ball A is dropped from rest and Ball B is launched horizontally at 12 m/s. Which ball reaches the floor first? Explain using the x/y independence of projectile motion.