Speed and Velocity, Work, Power and Energy
Workshop Calculation and Science, Module-5
Q1: What is the formula for speed?
- \(\frac{\text{Distance covered}}{\text{Time}}\)
- \(\frac{\text{Change in velocity}}{\text{Time}}\)
- \(\frac{\text{Distance in direction}}{\text{Time}}\)
- \(\frac{\text{Change in momentum}}{\text{Time}}\)
Q2: What is the unit of speed?
- Metre/second
- Metre/second²
- Metre/minute
- Metre/hour
Q3: What is the formula for velocity?
- \(\frac{\text{Distance covered}}{\text{Time}}\)
- \(\frac{\text{Displacement}}{\text{Time}}\)
- \(\frac{\text{Change in velocity}}{\text{Time}}\)
- \(\frac{\text{Change in momentum}}{\text{Time}}\)
Q4: What is the unit for velocity?
- Metre/second
- Metre/second²
- Metre/minute
- Metre/hour
Q5: What is called if a body possesses only magnitude?
- Speed
- Velocity
- Vector quantity
- Scalar quantity
Q6: What is called if a body possesses both magnitude and direction?
- Speed
- Velocity
- Vector quantity
- Scalar quantity
Q7: What is the rate of change of displacement of a body?
- Body at rest
- Body at motion
- Speed
- Velocity
Q8: What is called if a body does not change its position with respect to its surroundings?
- Body at motion
- Body at rest
- Speed
- Velocity
Q9: What is called if a body changes its position with respect to its surroundings?
- Body at rest
- Body at motion
- Speed
- Velocity
Q10: What is the velocity of a body that travels a distance of 168 metres in a line in 21 seconds?
- 6 m/s
- 8 m/s
- 10 m/s
- 12 m/s
Show Calculation
\[ \text{Velocity} = \frac{Distance}{Time} = \frac{168}{21} = 8\ \text{m/s} \]
Q11: What is the speed of a train of 80 metre long that passes a platform of 120 metres in 20 seconds?
- 30 km/h
- 32 km/h
- 34 km/h
- 36 km/h
Show Calculation
\[ \text{Total distance} = 80 + 120 = 200\ \text{m}\]\[ \\ \text{Speed} = \frac{200}{20} = 10\ \text{m/s}\] \[ = 10 \times \frac{18}{5} = 36\ \text{km/h} \] Show More
1 km = 1000 m
1 hr = 3600 s
1 km/h = 1000/3600 mps = 5/18 m/s
Similarly 1 m/s = 18/5 km/h
10 m/s = 10×18/5 km/h = 36 km/h
Q12: What is the formula for acceleration?
- \( a = \frac{v - u}{t} \)
- \( a = \frac{2v^2 - 2u^2}{t} \)
- \( a = \frac{2v^2 + 2u^2}{t} \)
- \( a = \frac{v + u}{t} \)
Q13: What is the unit of acceleration of an object?
- Metre/second
- Metre/second²
- Metre/minute
- Metre/minute²
Q14: What is the acceleration of a car if speed increases from 25 km/h to 40 km/h in 1 minute?
- 0.059 m/s²
- 0.59 m/s²
- 0.069 m/s²
- 0.69 m/s²
Show Calculation
Convert km/h to m/s: \[ u = 25 \times \frac{5}{18} = 6.94,\quad v = 40 \times \frac{5}{18} = 11.11 \\\] \[ a = \frac{11.11 - 6.94}{60} \approx 0.069\ \text{m/s}^2 \]
Q15: What is the retardation if a car moving at 50 km/h stops in 45 seconds?
- 0.40 m/s²
- 0.30 m/s²
- 0.20 m/s²
- 0.10 m/s²
Show Calculation
\[ u = 50 \times \frac{5}{18} = 13.89\ \text{m/s},\quad \] \[a = \frac{0 - 13.89}{45} = -0.30\ \text{m/s}^2 \]
Q16: What is the acceleration of an aeroplane that covers 700 metres in 10 seconds before take-off?
- 8 m/s²
- 10 m/s²
- 12 m/s²
- 14 m/s²
Show Calculation
Using: \[ s = \frac{1}{2}at^2 \] \[\Rightarrow 700 = \frac{1}{2}a \times 10^2 \] \[\Rightarrow a = \frac{1400}{100} = 14\ \text{m/s}^2 \]
Q17: What maximum height is reached by a stone thrown upwards at 20 m/s? (g = 10 m/s²)
- 10 m
- 20 m
- 30 m
- 40 m
Show Calculation
\[ v^2 = u^2 - 2gh \] \[\Rightarrow 0 = 400 - 2 \times 10 \times h \] \[\Rightarrow h = 20\ \text{m} \]
Q18: What is the work done in unit time called?
- Energy
- Power
- Force
- Acceleration
Show Explanation
Power is the rate of doing work: \[ P = \frac{W}{t} \]
Q19: What is the capacity of a body to do work called?
- Energy
- Power
- Acceleration
- Force
Q20: What is the ratio of power output to power input?
- Work
- Energy
- Efficiency
- Acceleration
Show Explanation
Efficiency is: \[ \text{Efficiency} = \frac{\text{Power Output}}{\text{Power Input}} \times 100\% \]
Q21: What is called if a force of 1 Newton acts on a body and moves it through a distance of 1 metre?
- 1 Joule
- 10 Joules
- 1 dyne
- 10 dynes
Show Explanation
Work is defined as: \[ W = F \times d = 1\ \text{N} \times 1\ \text{m} = 1\ \text{Joule} \]
Q22: How many ergs are there in 1 Joule?
- \(10^3\) ergs
- \(10^5\) ergs
- \(10^7\) ergs
- \(10^9\) ergs
Q23: How many newtons in 1 kilogram?
- 981 N
- 98.1 N
- 9.81 N
- 0.981 N
Show Calculation
\[ F = m \cdot g = 1 \cdot 9.81 = 9.81\ \text{N} \]
Q24: How many watts are in 1 horsepower (metric system)?
- 725.5 watts
- 735.5 watts
- 745.5 watts
- 755.5 watts
Q25: How many watts are in 1 horsepower (British system)?
- 726 watts
- 736 watts
- 746 watts
- 756 watts
Q26: What is the equivalent unit of 1 horsepower in the metric system?
- 75 kg·m/sec
- 76 kg·m/sec
- 77 kg·m/sec
- 78 kg·m/sec
Q27: What is the formula for potential energy?
- \(mgh\)
- \(mgh^2\)
- \(\frac{1}{2}mgh\)
- \(\frac{2}{3}mgh\)
Q28: What is the formula for kinetic energy?
- \(\frac{1}{2}mv\)
- \(\frac{1}{2}mv^2\)
- \(\frac{2}{3}mv^2\)
- \(\frac{2}{3}mv\)
Q29: How much work is done in 1 hour if a pump raises 100 L of water through 200 m in 1 minute?
- \(12 \times 10^4\) kg·m
- \(12 \times 10^5\) kg·m
- \(12 \times 10^6\) kg·m
- \(12 \times 10^7\) kg·m
Show Calculation
In 1 minute: \[ W = 100 \times 200 = 20000\ \text{kg·m} \] In 60 minutes: \[ 60 \times 20000 = 1.2 \times 10^6 = 12 \times 10^5\ \text{kg·m} \]
Q30: What is the work done if a force of 250 N moves a body through 15 m?
- 3720 J
- 3730 J
- 3740 J
- 3750 J
Show Calculation
\[ W = F \cdot d = 250 \cdot 15 = 3750\ \text{J} \]
Q31: What is the potential energy of a 250 kg object at 30 m height?
- 72.57 KJ
- 73.57 KJ
- 74.57 KJ
- 75.57 KJ
Show Calculation
\[ PE = mgh = 250 \cdot 9.81 \cdot 30 \] \[= 73575\ \text{J} = 73.575\ \text{KJ} \]
Q32: What is the potential energy of a 10 kg object on a 20 m pole?
- 1942 J
- 1952 J
- 1962 J
- 1972 J
Show Calculation
\[ PE = mgh = 10 \cdot 9.81 \cdot 20 = 1962\ \text{J} \]
Q33: What is the work done if a 15.5 kg load is lifted 4.4 metres?
- 639 J
- 649 J
- 659 J
- 669 J
Show Calculation
\[ W = mgh = 15.5 \cdot 9.81 \cdot 4.4 = 669.1\ \text{J} \]
Q34: What is the kinetic energy of a 5g bullet travelling at 500 m/s?
- 620 J
- 625 J
- 630 J
- 635 J
Show Calculation
Convert mass to kg: \(m = 5 \div 1000 = 0.005\ \text{kg}\)
\[ KE = \frac{1}{2}mv^2 = \frac{1}{2} \cdot 0.005 \cdot 500^2 = 625\ \text{J} \]