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Examples of Velocity and Distance Travel Calculations

Explore examples of calculating distance traveled based on velocity over time using constant and changing velocities over intervals. Includes detailed explanations and calculations. Improve your understanding of motion and displacement in physics.

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Examples of Velocity and Distance Travel Calculations

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  1. 3.1 Accumulated Changes Example 1: An objects travels with a velocity of 15 mph. What is the distance traveled after 4 hours The velocity is constant and the distance is: S = v.t = (4 ) (15) = 60 miles v Distance = area = (4)(15) =60 15 t 1 2 3 4

  2. Example 2: An objects travels for 4 hours with the following velocities: First hour : 15 mph, Second hour: 20 mph , Last 2 hours: 40 mph What is the distance traveled First hour : (15 mph)(1 hour) = 15 miles Total = 115 miles Second hour: (20 mph)(1 hour) = 20 miles Last 2 hours: (40 mph)(2 hours) = 80 miles v A=80 40 A=20 Distance = area = 15 + 20 + 80 = 115 miles 20 A=15 15 t 1 2 3 4

  3. Example 3: An objects travels with the following velocity: v = 15t + 10 Find the distance traveled after 4 hours 0 1 2 3 4 t Try t = 0,1,2,3,4 hours 10 25 40 55 70 v Total From Left: v (10)(1) + (40)(1) + (25)(1) + (55)(1) =130 70 70 55 55 40 40 25 25 10 t 1 2 3 4  = 1 hour

  4. Example 3 (Cont.): Using the same data and graph: Total From Left from previous slide: (10)(1) + (40)(1) + (25)(1) + (55)(1) =130 v 70 70 Total From Right: 55 55 (70)(1) + (40)(1) + (55)(1) + (25)(1) =190 40 40 25 Average: (130+190)/2 =160 miles 25 10 t 1 2 3 4  = 1 hour

  5. Note: • is the interval size n is the number of intervals v 70 70 70 55 55 55 40 40 40 25 25 25 10 t t 1 2 3 4 1 1.5 2 3 4 • = 1 hour n = 4 intervals • = 0.5 hour n = 8 intervals

  6. Example 4: An objects travels with the following velocity: v = 2t2 + 5 Find the distance traveled between t = 0 and t = 6 using n = 4 intervals 0 1.5 3 4.5 6 t • = 6 hours / 4 intervals =1.5 hour 23 77 5 9.5 45.5 v Total From Left: v 77 (5)(1.5) + (9.5)(1.5) + 45.5 (23)(1.5) + 23 (45.5)(1.5) + 9.5 =124.5 5 t 1.5 3 4.5 6  = 1.5 hour

  7. Example 4 (Cont.): Using the same data and graph: Total From Left from previous slide: =124.5 Total From Right: v 77 (77)(1.5) + (45.5)(1.5) + 45.5 (23)(1.5) + (9.5)(1.5) + 23 9.5 =232.5 5 t 1.5 3 4.5 6 Average: (124.5+232.5)/2 =178.5 miles  = 1.5 hour

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