# unit1 questions

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Unit 1 Question booklet1.1 1.2 1.3 1.4 1.5 1.6 Vectors Equations of Motion Newtons second law, Energy and Power Momentum and impulse density and pressure Gas Laws

ContentsRevision of speed an acceleration Page number 3

1.1

VectorsVector and scalers Past exam Questions: vector & scaler Adding Force Vectors Components Past exam question: vector anaylsis 5 7 8 10 12

1.2

Equations of MotionGraphs of Motion Past exam questions:graphs of motion Equations of Motion Past exam questions:equations of motion Projectiles Past exam questions:projectiles 16 20 27 29 34 36

1.3

Newtons second law, Energy and powerRevision of force, work and energy Past exam paper questions: Energy Force and acceleration Past exam questions:forces Past exam questions:forces on a slope 40 42 43 47 50

1.4

Momentum and ImpulseMomentum Past exam questions: momentum Impulse Past exam questions: impulse 53 56 62 64

1.5

Density & PressureDensity Past exam question: Density Pressure Pressure in liquids Past exam questions: Pressure Past exam questions: Upthrust and pressure in a liquid 68 69 70 71 73 77

1.6

Gas lawsPressure and Volume (constant temperature) Pressure and Temperature (constant volume) Temperature and Volume (constant pressure) General gas equation Past exam questions: Gas laws 79 81 82 83 84

2

Revision of Speed and Acceleration1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. What is meant by average speed? How would you measure the average speed of a bicycle? If you want to reach Edinburgh (290km away) in 3 hours, what must be your average speed? Why would you need to travel faster than that speed at some stages of your journey? It takes 2.5 hours to fly from Inverness to Southampton at an average speed of 370kmh-1. How far is Southampton from Inverness? How long will it take a walker to cover 1500m at a speed of 3.5ms-1? An athlete runs 800m in 1minute 53 seconds. What is her average speed? A snail moves at a speed of 0.001ms-1. How far will it travel in 1 hour? In orbit, a spacecraft takes 80 minutes to orbit the earth once, a distance of 50,800km. What is the speed of the spacecraft? What is meant by instantaneous speed? Describe how you would measure the instantaneous speed of a trolley near the bottom of a runway. A hand operated digital stopwatch is suitable for measuring the average speed of a runner, but should not be used to measure the instantaneous speed. Explain why not. The following is a record of a journey using public transport.

(i)

1.0km at 4.0kmh-1, walking (ii) 10 minute wait (iii) 32km at 48kmh-1, by bus (iv) 45 minute wait

(v) plane

2400km at 800kmh-1, by

(vi) 30 minute wait (vii) 50km at 100kmh-1, by coach (viii) 20 minute wait

(a) (b) (c) 13.

How long did the journey take? How far was the journey? What was the average speed?

A cars motion is described in the graph shown below. (a) (b) What is the cars average speed over the 12 seconds? What is its instantaneous speed at 8.0s?

3

14. 15. 16. 17. 18. 19. 20.

What is meant by acceleration? Write down the formula used to calculate acceleration and explain what the symbols mean. Describe how you would measure the acceleration of a vehicle. A car is travelling at 8.0ms-1 and accelerates to 24ms-1 in 4.0 seconds. What is its acceleration? An archer releases an arrow and it attains a speed of 50ms-1 having accelerated at 400ms-2. How long did the acceleration take? A lorry brakes with an acceleration of -4.5ms-2 and takes 10 seconds to reduce its speed to What was its initial speed? A plane is flying at a speed of 250ms-1 and accelerates for 8 seconds at 6.7ms-2. speed? Sketch a speed-time graph for each of the following motions. (a) (b) (c) 21. (a) (b) (c) (d) (e) (f) Steady speed. Speeding up uniformly. Slowing down uniformly. Use the graph to find the following. The acceleration between C and D The deceleration between A and B Distance travelled in the first 4 seconds. Distance travelled between 4 and 9 seconds. Distance travelled between 9 and 11 seconds. Average speed for the whole journey. B C A D 10ms-1.

What is its final

4

Scalars and Vectors1. Divide the following quantities into two lists, one scalars and the other vectors. mass; speed; area; distance; velocity; displacement; time; acceleration 2. 3. 4. What is your displacement if you fly 50km NE from Dalcross, then 100km NW? Find your displacement if you walk 100m east, then 30m south west, and finally 80m north. A yacht sails due west for 6km, then due north for 8km. It takes 3 hours. (a) (b) (c) (d) 5. What distance has it travelled? What is its final displacement? What is its average speed? What is its average velocity?

A mine locomotive travels 1 km from the top of a mineshaft to the coal tip and back again. The tip is due east of the mine. What is the locomotives final displacement? If the journey takes 10 minutes in each direction, calculate its average speed and its average velocity in ms-1. A cyclist rides 6km NW, 6km S, then turns west and cycles a further 10km. The journey takes her a total of 1.4 hours. (a) (b) (c) (d) What distance has she travelled? What is her final displacement? What is her average speed? What is her average velocity?

6.

7. 8.

A passenger walks 20m north across the deck of ship. During this time the ship moves 60m east. Find the passenger's final displacement relative to the earth. An aircraft takes off from Dalcross and flies along compulsory 'air corridors' to its destination. The 'legs' of its journey are as follows. 180 for 100km; 125 for 88 km; 055 for 65 km; 164 for 175 km Find the aircraft's final displacement at the end of the journey.

9.

A trawler sets out from Aberdeen and steams 45 km east, then 16 km on a heading of 200o. The skipper then decides to give up fishing and head for home but has only gone 5 km when the engine breaks down. A tug sets out to rescue the trawler. In what direction should the tug proceed and how far will it have to travel before reaching the trawler. In practice the direction and distance may be different. Why could this be so?

10.

In an orienteering competition, a competitor at point X decides to go first to point Z then point Y. The location of these points is shown in the diagram. (The diagram is not to scale.) (a) What is the displacement form Z to Y? (b) (c) (d) What total distance does the orienteer travel? If she runs at a steady speed of 5ms-1, how long did it take her? What is her velocity from Z to Y?

11.

A model plane is flying due north with a velocity of 24ms-1 when it is subjected to a gust of wind blowing from west to east at 10ms-1. What is the resultant velocity of the plane? 5

12.

A motorboat can travel at 3ms-1 through the water. It is going to cross a river that flows at 2ms-1 If the boat sets off directly for the opposite bank, find (a) (b) (c) its resultant velocity, its final displacement if the river is 50m wide, the time taken to reach the far bank.

13.

On a day when there was a wind blowing of 50kmh-1 from the south, a helicopter pilot flew at 200kmh-1 due east towards an oil platform located 300km due east of Sumburgh. When the pilot was due north of the platform, how far had he travelled and how long had this taken him? A skier is skiing forward at 20kmh-1 across the slope of a hillside. She then begins to slip sideways at a speed of 4kmh-1 as well as continuing forward at her original velocity. What is her resultant velocity? A hovercraft leaves Dover and sets course SE at 12ms-1. A wind is blowing from the NE that carries the hovercraft sideways at 5ms-1. What velocity should the Captain now set to return to the original velocity? A boat sails a course in the following order: a) Due North for 15km c) Due South for 10km b) Due West for 5km d) South East for 7km Using the information above, draw a scale diagram to find out the displacement of the boat from its starting point. A plane takes off from an airfield and flies at a bearing of 500 for a total distance of 100 nautical miles. It turns to a bearing of 3400 for a further distance of 60 miles. Turning now to a bearing of 1350, it flies for a distance of 50 miles before turning and flying for home. By using a scale drawing estimate the bearing and the distance of its last leg to the airfield. A boy walks around a rectangle of dimensions 100m by 50m. If he makes one complete circuit in 100s, calculate: a) Total distance travelled c) Displacement b) Average speed d) Average velocity A car travels 50km North and then returns 30km South. The whole journey takes 2 hours. Calculate: a) Total distance travelled c) Displacement b) Average speed d) Average velocity An aircraft has a maximum speed of 1000kmh-1. If it is flying into a head wind of speed100kmh-1, what is the velocity of the aircraft relative to the ground? A model aircraft is flying North with a velocity of 24ms-1. A wind is blowing from West to East at 10ms-1. What is the resultant velocity of the plane? An aircraft pilot wishes to fly North at 800kmh-1. A wind is blowing at 80kmh-1 from West to East. What speed and course must he select in order to fly the desired course? A girl delivers newspapers to three houses X, Y and Z as shown in the diagram, starting at X. The girl walks directly from one house to the next. a) Find the total distance the girl walks. b) Calculate the girls final displacement from X. c) If the girl walks at 1ms-1, calculate the time she takes to get from X to Z. d) Calculate her resultant velocity. A train is crossing a bridge at 40kmh-1 north and a boat passing below the bridge at 20kmh-1 west. What is the velocity of the train relative to the boat? 6

14. 15.

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