HCI Worksheet 7 Vectors and Kinematics (answers)

Hwa Chong Institution Sec 3 Physics 1 Name: ________________________________________ Class: __________ Date: ___________ Sec 3 Physics Worksheet 7: Vectors & 1-D Kinematics SECTION A: CONCEPTUAL QUESTIONS 1. Does a car speedometer measure speed, velocity or both? A speedometer measures the speed. 2. Can an object have a varying speed if its velocity is constant? If yes, give examples. No. Constant velocity means that the magnitude and direction components are constant, as such, a varying speed is impossible. 3. When an object moves with constant velocity, does its av erage velocity during any time interval differ from its instantaneous velocity at any instant? No. Average velocity = instantaneous velocity = constant velocity 4. If object A has a greater speed than object B, does object A necessarily have a greater acceleration? No, speed and acceleration are two different physical quantities. We can give many counter- examples. E.g. A is thrown vertically downwards while B is dropped from rest at the same time; both objects will have the same acceleration but A will have a greater speed. 5. As a freely falling object speeds up, what is happening to its acceleration due to gravity – does it increase, decrease or stay the same? Acceleration stays constant at 9.81 ms-2. 6. Can an object have zero velocity and non-zero acceleration at the same time? Give examples. Yes. An object thrown vertically upwards will have a zero velocity at the maximum height (turning point) but its acceleration at any instant is 9.81 m s-2 downwards. (The object is free- falling even if it is being thrown upwards.) 7. Can an object have zero acceleration and non -zero velocity at the same time? Give examples. Yes, any object undergoing constant velocity satisfies the condition.

Hwa Chong Institution Sec 3 Physics 2 8. *Describe in words, the motion plotted in Figure 1 in terms of v, a etc. [Hint: try to think about the slope of the graph and how the slope varies with time.] Figure 1 t = 0 to t = 20s: Displacement: increases from 0 to about 6 m. Velocity: constant at about 0.3 m s-1. Acceleration is zero. t = 20s to t = 27.5s Displacement increases to about 12 m. Velocity is increasing and positive with respect to displacement. Acceleration is positive with respect to displacement. t = 27.5s to t = 37.5s Displacement increases to 20 m. Velocity is decreasing but still positive with respect to displacement. At t = 37.5 s, velocity is zero. Acceleration is negative with respect to displacement. t = 37.5s to t = 45 s Displacement decreases to about 15 m. Magnitude of velocity is increasing and negative with respect to displacement. Acceleration is negative with respect to displacement. t = 45s to t = 50s Displacement decreases to 10 m. Velocity is increasing but still negative with respect to displacement. Acceleration is positive with respect to displacement.

Hwa Chong Institution Sec 3 Physics 3 9. **Describe in words, the motion of the object graphed in Figure 2. Figure 2 t = 0 to t = 30s Displacement increases to about   1 15 30 30 675 m2  and positive with respect to velocity. Velocity increases linearly from about 15 m s-1 to 30 m s-1. Acceleration is constant and positive with respect to velocity. t = 30s to t = 50s Displacement increases to about 1350 m. (Estimate by area of squares) Velocity is still increasing and reaches a maximum of about 38 m s-1 at about t = 48s. Acceleration is decreasing but positive with respect to velocity. t = 50s to t = 70s Displacement continues to increase to about 1930 m. (Estimate by area of squares) Velocity is decreasing and is about 20 m s-1 at t = 70 s. Acceleration is decreasing and negative with respect to velocity. t = 70s to t = 90s Displacement continues to increase to about 2130 m. (Estimate by area of squares) Velocity is decreasing and is zero at t = 90 s. Acceleration is decreasing and negative with respect to velocity. t = 90s to t ~ 107s Displacement remains at about 2130 m. (object stops) Velocity is zero. Acceleration is zero. t ~ 107s to t = 125s Displacement increases to about 2230 m. (Area estimate) Velocity increases to about 11 m s-1. Acceleration has a decreasing trend and is positive with respect to

Hwa Chong Institution Sec 3 Physics 4 velocity. 10. Sometimes, a word used in layman’s speech can be different when it is used in a Physics context. Explain how the words inertia and acceleration can mean differently when used in Physics and in layman’s speech. Inertia in layman’s speech often refers to a state of rest or a state of reluctance to move / act. In Physics, the law of inertia describes the motion of objects either in a state of rest or moving with constant velocity; the latter state is not used in layman’s speech. Acceleration in layman’s speech is often associated with objects moving faster and faster. In Physics, acceleration can refer to both the object speeding up or slowing down.

Hwa Chong Institution Sec 3 Physics 5 SECTION B: STRUCTURED QUESTIONS 1 An airplane travels 3100 km at a speed of 790 km h -1, and then encounters a tailwind that boosts its speed to 990 km h-1 for the next 2800 km. a What was the total time for the trip? 3100 2800Total time 790 990 6.8 h   b What was the average speed of the airplane for the trip? 1 Total distance Total time 3100 2800 6.8 874 870 km h (corrected to 2sf)     v 2 *A car travelling 88 km h -1 is 110 m behind a truck travelling 75 km h -1. How long will it take the car to reach the truck?   1 88 75Relative speed 3.6 3.61 m s   Relative distanceTime taken to overtake Relative speed 110 3.61 30 s (corrected to 2sf)    3 ** A bowling ball travelling with a constant speed hits the pins at the end of a bowling lane 16.5 m long. The bowler hears the sound of the ball hitting the pins 2.50 s after the ball is released from his hands. What is the speed of the ball? The speed of sound is 340 m s-1. 16.5Time taken for the ball to roll 2.50 340 2.451 s   1 Length of bowling laneSpeed of the ball Time taken for ball to roll 16.5 2.451 6.73 m s (corrected to 3sf)   

Hwa Chong Institution Sec 3 Physics 6 4 *At highway speeds, a particular automobile is capable of an acceleration of about 1.6 m s-2. At this rate, how long does it take to accelerate from 80 km h-1 to 110 km h-1?     Acceleration 110 80 3.61.6 110 80 3.6 1.6 5.2 s (corrected to 2sf) v t t t       5 A car accelerates from 13 m s-1 to 25 m s-1 in 6.0 s. Assume constant acceleration. a What was its acceleration? 2 25 13 6.0 2.0 m s     va t b How far did it travel in this time?       2 2 1 2 113 6.0 2.0 6.02 114 m (since the last operation is addition, we looked to the decimal place) s ut at   6 A car travelling 85 km h -1 strikes a tree. The front end of the car compresses and the driver comes to rest after travelling 0.80 m. What was the average acceleration of the driver during the collision? Express the answer in terms of “g’s” where 1.00 g = 9.81m s-2.    22 2 2 -2 -2 2 850 2 0.803.6 350 ms 350 ms 9.81 ms 36 g       v u as a a

Hwa Chong Institution Sec 3 Physics 7 7 ** A falling stone takes 0.28 s to t