Speed = Distance /Time Questions

Answers to Speed = Distance/Time Questions

1. Speed = 100 ÷ 12.5 = 8.0 m/s
2. Speed = 2400 ÷ 360 = 6.7 m/s
3. Speed = 1800 ÷ 240 = 7.5 m/s
4. Distance = 18 × 150 = 2700 m
5. Time = 12000 ÷ 10 = 1200 s (20 min)
6. Distance = 4.5 × 40 = 180 m
7. Time = 72 ÷ 3.0 = 24 s
8. Speed = 9000 ÷ 720 = 12.5 m/s
9. Speed = 1800 ÷ 24 = 75 m/s

10a Time = 54000 ÷ 60 = 900 s

10b Time = 900 ÷ 60 = 15 min

Challenge: Speed = (4.2 × 10⁷) ÷ (3.5 × 10⁴) = 1.2 × 10³ m/s = 1200 m/s

17 Questions using v² = u² + 2as

Answers to v² = u² + 2as Questions

1. v² = 2² + (2 × 1.5 × 16) = 52, so v = 7.2 m/s.
2. v² = 4² + (2 × 2 × 24) = 112, so v = 10.6 m/s.
3. v² = 8² + (2 × 1.5 × 48) = 208, so v = 14.4 m/s.
4. v² = 10² + (2 × 3 × 75) = 550, so v = 23.5 m/s.
5. v² = 12² + (2 × 5 × 80) = 944, so v = 30.7 m/s.
6. v² = 0² + (2 × 1 × 800) = 1600, so v = 40 m/s.
7. a = (70² – 30²) ÷ (2 × 500) = 4 m/s².
8. a = (32² – 12²) ÷ (2 × 220) = 2 m/s².
9. a = (11² – 5²) ÷ (2 × 24) = 2 m/s².
10. a = (0² – 20²) ÷ (2 × 40) = -5 m/s², so deceleration = 5 m/s².
11. a = (0² – 14²) ÷ (2 × 28) = -3.5 m/s², so deceleration = 3.5 m/s².
12. a = (0² – 35²) ÷ (2 × 490) = -1.25 m/s², so deceleration = 1.25 m/s².
13. s = (0² – 25²) ÷ (2 × -6.25) = 50 m.
14. s = (0² – 80²) ÷ (2 × -2) = 1600 m.
15. a = (150² – 0²) ÷ (2 × 750) = 15 m/s².
16. u² = 42² – (2 × 3.5 × 210) = 294, so u = 17.1 m/s.

17a. a = (0² – 90²) ÷ (2 × 1800) = -2.25 m/s², so deceleration = 2.25 m/s².

17b. s = (0² – 90²) ÷ (2 × -1.5) = 2700 m.

17c. Reducing stopping distance is important because the train stops sooner, reducing the chance of a collision.

10 Ramped Questions on Calculating acceleration

Answers to acceleraiton Questions

1. Acceleration = (5 – 1) ÷ 4 = 1 m/s².
2. Acceleration = (10 – 0) ÷ 8 = 1.25 m/s².
3. Acceleration = (12 – 4) ÷ 5 = 1.6 m/s².
4. Acceleration = (44 – 20) ÷ 3 = 8 m/s².
5. Acceleration = (32 – 8) ÷ 6 = 4 m/s².
6. Final velocity = 0 + (2.5 × 12) = 30 m/s.
7. Final velocity = 5 + (1.5 × 20) = 35 m/s.
8. 18 km/h = 5 m/s and 72 km/h = 20 m/s, so acceleration = (20 – 5) ÷ 10 = 1.5 m/s².
9. Time = (90 – 30) ÷ 4 = 15 s.
10. a) Acceleration = (360 – 0) ÷ 30 = 12 m/s².

12 Questions on F=ma (Resultant force F also has to be calculated)

Answers to F=ma resultant force questions

1. Resultant force = 80 – 30 = 50 N, so acceleration = 50 ÷ 25 = 2 m/s².
2. Resultant force = 180 – 60 = 120 N, so acceleration = 120 ÷ 75 = 1.6 m/s².
3. Resultant force = 250 – 100 = 150 N, so acceleration = 150 ÷ 50 = 3 m/s².
4. Resultant force = 900 – 300 = 600 N, so acceleration = 600 ÷ 400 = 1.5 m/s².
5. Resultant force = 5000 – 2000 = 3000 N, so acceleration = 3000 ÷ 1250 = 2.4 m/s².
6. Resultant force = 1500 – 4500 = -3000 N, so deceleration = 3000 ÷ 1500 = 2 m/s².
7. Resultant force = 100000 – 40000 = 60000 N, so acceleration = 60000 ÷ 80000 = 0.75 m/s².

8a. Resultant force = 20000 – 140000 = -120000 N.

8b. Deceleration = 120000 ÷ 60000 = 2 m/s².

9a. Resultant force = 12000 – 2000 = 10000 N.

9b. Acceleration = 10000 ÷ 1000 = 10 m/s².

9c. Final velocity = 8 + (10 × 5) = 58 m/s.

10a. Resultant force = 750000 – 250000 = 500000 N.

10b. Acceleration = 500000 ÷ 25000 = 20 m/s².

10c. Final velocity = 0 + (20 × 20) = 400 m/s.

11a. Resultant force = -(18000 + 2000) = -20000 N.

11b. Deceleration = 20000 ÷ 800 = 25 m/s².

11c. Final velocity = 72 – (25 × 2) = 22 m/s.

12a. Resultant force = 50000 – 250000 = -200000 N.

12b. Deceleration = 200000 ÷ 200000 = 1 m/s².

12c. Final velocity = 30 – (1 × 10) = 20 m/s.

12d. No, because after 10 s the train is still travelling at 20 m/s.

Momentum Calculations using mv

Answers to Momentum Questions

1. p = mv = 0.45 × 10 = 4.5 kg m/s
2. p = mv = 80 × 5 = 400 kg m/s
3. p = mv = 25 × 2.5 = 62.5 kg m/s
4. p = mv = 200 × 12 = 2400 kg m/s
5. p = mv = 300 × 4 = 1200 kg m/s
6. p = mv = 1800 × 15 = 27 000 kg m/s
7. p = mv = 25 000 × 20 = 500 000 kg m/s
8. v = p ÷ m = 18 000 ÷ 900 = 20 m/s
9. m = p ÷ v = 50 000 ÷ 25 = 2000 kg
10. v = p ÷ m = 180 000 ÷ 12 000 = 15 m/s

17 Conservation of Momentum Ramped Questions

Answers to Conservation of Momentum Questions

1. Total mass = 3 kg, total momentum = 6 kg m/s, so v = 6 ÷ 3 = 2 m/s
2. Momentum transfers to second ball, so v = 8 m/s
3. Total mass = 80 kg, total momentum = 240 kg m/s, so v = 240 ÷ 80 = 3 m/s
4. Total mass = 1500 kg, total momentum = 10 000 kg m/s, so v = 10 000 ÷ 1500 = 6.7 m/s
5. Total mass = 120 kg, total momentum = 350 kg m/s, so v = 350 ÷ 120 = 2.9 m/s
6. Total mass = 75.15 kg, total momentum = 4.5 kg m/s, so v = 4.5 ÷ 75.15 = 0.060 m/s
7. Total mass = 2000 kg, total momentum = 18 000 kg m/s, so v = 18 000 ÷ 2000 = 9 m/s
8. Total mass = 3000 kg, total momentum = 24 000 kg m/s, so v = 24 000 ÷ 3000 = 8 m/s
9. Bag momentum = 5 × 8 = 40 kg m/s backwards, so canoeist momentum = 40 kg m/s forwards and v = 40 ÷ 75 = 0.53 m/s forwards
10. Tool momentum = 2 × 15 = 30 kg m/s forwards, so astronaut momentum = 30 kg m/s backwards and v = 30 ÷ 50 = 0.6 m/s backwards
11. Total momentum = 30 000 + 5000 = 35 000 kg m/s, total mass = 2500 kg, so v = 14 m/s
12. Total momentum = 21 600 − 8000 = 13 600 kg m/s east, total mass = 2000 kg, so v = 6.8 m/s east
13. Change in momentum = 0.2 × (-15 − 25) = -8 kg m/s, so the size of the change is 8 kg m/s
14. Total momentum = 18 000 − 8000 = 10 000 kg m/s east, total mass = 2500 kg, so v = 4 m/s east
15. Total momentum = 1000 − 400 = 600 kg m/s, total mass = 450 kg, so v = 1.3 m/s in the first dodgem’s direction
16. Total mass = 5000 kg, total momentum = 18 000 kg m/s, so v = 18 000 ÷ 5000 = 3.6 m/s
17. Total momentum = 24 000 − 15 000 = 9000 kg m/s, total mass = 2700 kg, so v = 3.3 m/s in the electric car’s direction