Physics: Principles with Applications
Physics: Principles with Applications
6th Edition
ISBN: 9780130606204
Author: Douglas C. Giancoli
Publisher: Prentice Hall
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Chapter 2, Problem 20P

(a)

To determine

To find: The velocity of the car as a function of time.

(a)

Expert Solution
Check Mark

Explanation of Solution

Given:

      t(s)  x(m)
    00
    0.250.11
    0.500.46
    0.751.06
    1.001.94
    1.504.62
    2.008.55
    2.5013.79
    3.0020.36
    3.5028.31
    4.0037.65
    4.5048.37
    5.0060.30
    5.5073.26
    6.0087.16

Formula used:

  v=ΔxΔt=x2x1t2t1

Where,

  v= Velocity of the car.

  Δx= Displacement of the car.

  Δt= Time interval.

Calculation:

Velocity of the car between interval 0 s0.25 s :

  v1=0.110.000.250=0.44 m/s

The car has this velocity at the midpoint of the interval. i.e. (0.0+0.252=1.25 s)

Velocity of the car between interval 0.25 s0.5 s :

  v2=0.460.110.50.25=1.4 m/s

  t'(s)

The car has this velocity at the midpoint of the interval, 0.375 s

      t(s)

      x(m)

      t'(s)

      V(m/s)

    0 0 0 0.00
    0.25 0.11 0.125 0.44
    0.50 0.46 0.375 1.40
    0.75 1.06 0.625 2.40
    1.00 1.94 0.875 3.52
    1.50 4.62 1.25 5.36
    2.00 8.55 1.75 7.86
    2.50 13.79 2.25 10.48
    3.00 20.36 2.75 13.14
    3.50 28.31 3.25 15.90
    4.00 37.65 3.73 18.68
    4.50 48.37 4.25 21.44
    5.00 60.30 4.75 23.86
    5.50 73.26 5.25 25.92
    6.00 87.16 5.72 27.80

The plot of velocity vs timePhysics: Principles with Applications, Chapter 2, Problem 20P , additional homework tip  1

Conclusion:

Hence, the velocity in m/s as a function of time is:

  0.00,0.44,1.40,2.40,3.52,5.36,7.86,10.48,13.14,15.90,18.68,21.44,23.86,25.92,27.80

(b)

To determine

To find: The acceleration of the car as a function of time.

(b)

Expert Solution
Check Mark

Explanation of Solution

Given:

      t'(s)

      V(m/s)

    00.00
    0.1250.44
    0.3751.40
    0.6252.40
    0.8753.52
    1.255.36
    1.757.86
    2.2510.48
    2.7513.14
    3.2515.90
    3.7318.68
    4.2521.44
    4.7523.86
    5.2525.92
    5.72 27.80

Formula used:

  a=ΔVΔt=V2V1t2t1

Where,

  a= Acceleration of the car.

  ΔV= change in the velocity.

  Δt= Time interval.

Calculation:

Acceleration of the car between 0 s0.125 s :

  a1=0.440.000.1250.00=3.52 m/s2

The car has this acceleration at the midpoint of time interval. i.e. (0.0+0.1252=0.063 s)

Therefore, the table of acceleration as the function of time:

      t'(s)

      V(m/s)

      t''(s)

      a(m/s2)

    00.000.00 0
    0.1250.440.063 3.52
    0.3751.400.25 3.84
    0.6252.400.50 4.00
    0.8753.520.75 4.48
    1.255.361.06 4.91
    1.757.861.50 5.00
    2.2510.482.00 5.24
    2.7513.142.50 5.32
    3.2515.903.00 5.52
    3.7318.683.50 5.56
    4.2521.444.00 5.52
    4.7523.864.50 4.84
    5.2525.925.00 4.12
    5.72 27.805.50 3.76

The plot of acceleration vs time:

  Physics: Principles with Applications, Chapter 2, Problem 20P , additional homework tip  2 Conclusion:

Hence, the acceleration in m/s2 as a function of time is:

  0,3.52,3.84,4.00,4.48,4.91,5.00,5.24,5.52,5.56,5.52,4.84,4.12,3.76

Chapter 2 Solutions

Physics: Principles with Applications

Ch. 2 - Can an object be increasing in speed as its...Ch. 2 - A baseball player hits a ball straight up into the...Ch. 2 - As a freely falling object speeds up, what is...Ch. 2 - Prob. 14QCh. 2 - You travel from point A to point B in a car moving...Ch. 2 - Prob. 16QCh. 2 - Prob. 17QCh. 2 - Prob. 18QCh. 2 - Prob. 19QCh. 2 - Prob. 20QCh. 2 - Describe in words the motion plotted in Fig. 2-32...Ch. 2 - Describe in words the motion of the object graphed...Ch. 2 - Prob. 1PCh. 2 - Prob. 2PCh. 2 - Prob. 3PCh. 2 - Prob. 4PCh. 2 - Prob. 5PCh. 2 - Prob. 6PCh. 2 - Prob. 7PCh. 2 - Prob. 8PCh. 2 - Prob. 9PCh. 2 - Prob. 10PCh. 2 - Prob. 11PCh. 2 - Prob. 12PCh. 2 - Prob. 13PCh. 2 - Prob. 14PCh. 2 - Prob. 15PCh. 2 - A sports car accelerates from rest to 95 km/h in...Ch. 2 - Prob. 17PCh. 2 - Prob. 18PCh. 2 - 19.(II) A sports car moving at constant velocity...Ch. 2 - Prob. 20PCh. 2 - Prob. 21PCh. 2 - Prob. 22PCh. 2 - Prob. 23PCh. 2 - Prob. 24PCh. 2 - Prob. 25PCh. 2 - Prob. 26PCh. 2 - Prob. 27PCh. 2 - Prob. 28PCh. 2 - Prob. 29PCh. 2 - Prob. 30PCh. 2 - Prob. 31PCh. 2 - Prob. 32PCh. 2 - Prob. 33PCh. 2 - Prob. 34PCh. 2 - Prob. 35PCh. 2 - Prob. 36PCh. 2 - Prob. 37PCh. 2 - Prob. 38PCh. 2 - Prob. 39PCh. 2 - Prob. 40PCh. 2 - Prob. 41PCh. 2 - Prob. 42PCh. 2 - Prob. 43PCh. 2 - Prob. 44PCh. 2 - Prob. 45PCh. 2 - Prob. 46PCh. 2 - Prob. 47PCh. 2 - Prob. 48PCh. 2 - Prob. 49PCh. 2 - Prob. 50PCh. 2 - Prob. 51PCh. 2 - Prob. 52PCh. 2 - Prob. 53PCh. 2 - Prob. 54PCh. 2 - Prob. 55PCh. 2 - Prob. 56PCh. 2 - Prob. 57GPCh. 2 - Prob. 58GPCh. 2 - Prob. 59GPCh. 2 - Prob. 60GPCh. 2 - Prob. 61GPCh. 2 - Prob. 62GPCh. 2 - Prob. 63GPCh. 2 - Prob. 64GPCh. 2 - Prob. 65GPCh. 2 - Prob. 66GPCh. 2 - Prob. 67GPCh. 2 - Prob. 68GPCh. 2 - Prob. 69GPCh. 2 - Prob. 70GPCh. 2 - Prob. 71GPCh. 2 - Prob. 72GPCh. 2 - Prob. 73GPCh. 2 - Prob. 74GPCh. 2 - Prob. 75GPCh. 2 - Prob. 76GPCh. 2 - Prob. 77GPCh. 2 - Prob. 78GPCh. 2 - Prob. 79GPCh. 2 - Prob. 80GPCh. 2 - Prob. 81GPCh. 2 - Prob. 82GPCh. 2 - Prob. 83GPCh. 2 - Prob. 84GPCh. 2 - Prob. 85GP
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Position/Velocity/Acceleration Part 1: Definitions; Author: Professor Dave explains;https://www.youtube.com/watch?v=4dCrkp8qgLU;License: Standard YouTube License, CC-BY