2020 - Day 5 - Average Speed & Average Velocity - Presentation

Average Speed vs. Average Velocity

  • Average Velocity:

    • Definition: Rate of change of position (displacement).

    • Calculation: Resultant displacement divided by total time.

    • Nature: Vector quantity, which means it has both magnitude and direction.

  • Average Speed:

    • Definition: Rate of the total distance traveled.

    • Calculation: Total distance traveled divided by total time.

    • Nature: Scalar quantity, which means it only has magnitude.

Sample Problems

Problem 1: Motorcycle Average Speed

  • Information Given:

    • Distance traveled: 70 km in 1.2 h, then stops for 0.30 h, then 100 km in 1.0 h.

  • Total Distance: 70 km + 100 km = 170 km.

  • Total Time: 1.2 h + 0.3 h + 1.0 h = 2.5 h.

  • Average Speed Calculation:

    • Formula: ( V_{avg} = \frac{d_{total}}{t_{total}} )

    • Calculation: ( V_{avg} = \frac{170 \text{ km}}{2.5 \text{ h}} = 68 \text{ km/h} )

Problem 2: Aircraft Range

  • Information Given:

    • Cruising speed: 435 km/h.

    • Fuel consumption: 45 L/h.

    • Fuel tank capacity: 225 L.

  • Total Time of Flight Calculation:

    • Total time = ( \frac{225 \text{ L}}{45 \text{ L/h}} = 5 \text{ h} )

  • Range Calculation:

    • Formula: ( d = V \times t )

    • Calculation: ( d = 435 \text{ km/h} \times 5 \text{ h} = 2175 \text{ km} )

Problem 3: Maham's Running Speed

  • Information Given:

    • Average speed 1: 12 km/h for the first 10 km.

    • Average speed 2: 8 km/h for the last 10 km.

  • Total Distance: 20 km.

  • Average Speed Calculation:

    • Time for first segment: ( t_1 = \frac{10 \text{ km}}{12 \text{ km/h}} \approx 0.83 \text{ h} )

    • Time for second segment: ( t_2 = \frac{10 \text{ km}}{8 \text{ km/h}} = 1.25 \text{ h} )

    • Total time: ( t_{total} = t_1 + t_2 \approx 2.08 \text{ h} )

    • Average speed: ( V_{avg} = \frac{20 \text{ km}}{2.08 \text{ h}} \approx 9.62 \text{ km/h} )

Problem 4: Nicole's Baseball Performance

  • Information Given:

    • Time to round first base: 3.5 s.

    • Time to reach third base from home plate: 10 s.

    • Distance between bases: 27.4 m.

  • Average Speed Calculation:

    • Total Distance: 54.8 m (considering right angle).

    • Total Time: 10 s - 3.5 s = 6.5 s.

    • Average speed: ( V_{avg} = \frac{54.8 , m}{6.5 , s} \approx 8.43 , m/s )

Problem 5: Mohammed’s Boxing Training

  • Information Given:

    • First Leg: Runs north at 16 km/h for 8 km, returns to training camp at 10 km/h.

Part (a): Average Speed Calculation

  • Distance: Total distance = 8 km + 8 km = 16 km.

  • Time Calculation:

    • Time for first leg: ( t_1 = \frac{8 , km}{16 , km/h} = 0.5 , h )

    • Time for return leg: ( t_2 = \frac{8 , km}{10 , km/h} = 0.8 , h )

    • Total Time: 1.3 h.

  • Average Speed: ( V_{avg} = \frac{16 , km}{1.3 , h} \approx 12.31 , km/h )

Part (b): Average Velocity Calculation

  • Average velocity considers direction, while speed does not. Calculation accounts for displacement.