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authorprashantsinalkar2017-10-10 12:27:19 +0530
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-rw-r--r--3472/CH43/EX43.1/Example43_1.sce28
-rw-r--r--3472/CH43/EX43.10/Example43_10.sce29
-rw-r--r--3472/CH43/EX43.11/Example43_11.sce34
-rw-r--r--3472/CH43/EX43.12/Example43_12.sce27
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-rw-r--r--3472/CH43/EX43.3/Example43_3.sce29
-rw-r--r--3472/CH43/EX43.4/Example43_4.sce32
-rw-r--r--3472/CH43/EX43.5/Example43_5.sce26
-rw-r--r--3472/CH43/EX43.6/Example43_6.sce36
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diff --git a/3472/CH43/EX43.1/Example43_1.sce b/3472/CH43/EX43.1/Example43_1.sce
new file mode 100644
index 000000000..2f257d607
--- /dev/null
+++ b/3472/CH43/EX43.1/Example43_1.sce
@@ -0,0 +1,28 @@
+// A Texbook on POWER SYSTEM ENGINEERING
+// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar
+// DHANPAT RAI & Co.
+// SECOND EDITION
+
+// PART IV : UTILIZATION AND TRACTION
+// CHAPTER 5: ELECTRIC TRACTION-SPEED TIME CURVES AND MECHANICS OF TRAIN MOVEMENT
+
+// EXAMPLE : 5.1 :
+// Page number 778
+clear ; clc ; close ; // Clear the work space and console
+
+// Given data
+speed = 45.0 // Scheduled speed(kmph)
+D = 1.5 // Distance between 2 stops(km)
+t = 20.0 // Time of stop(sec)
+alpha = 2.4 // Acceleration(km phps)
+beta = 3.2 // Retardation(km phps)
+
+// Calculations
+t_total = D*3600/speed // Total time(sec)
+T = t_total-t // Actual time for run(sec)
+k = (alpha+beta)/(alpha*beta) // Constant
+V_m = (T/k)-((T/k)**2-(7200*D/k))**0.5 // Maximum speed over the run(kmph)
+
+// Results
+disp("PART IV - EXAMPLE : 5.1 : SOLUTION :-")
+printf("\nMaximum speed over the run, V_m = %.f kmph", V_m)
diff --git a/3472/CH43/EX43.10/Example43_10.sce b/3472/CH43/EX43.10/Example43_10.sce
new file mode 100644
index 000000000..b44ae441e
--- /dev/null
+++ b/3472/CH43/EX43.10/Example43_10.sce
@@ -0,0 +1,29 @@
+// A Texbook on POWER SYSTEM ENGINEERING
+// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar
+// DHANPAT RAI & Co.
+// SECOND EDITION
+
+// PART IV : UTILIZATION AND TRACTION
+// CHAPTER 5: ELECTRIC TRACTION-SPEED TIME CURVES AND MECHANICS OF TRAIN MOVEMENT
+
+// EXAMPLE : 5.10 :
+// Page number 784
+clear ; clc ; close ; // Clear the work space and console
+
+// Given data
+W = 350.0 // Weight of train(tonne)
+G = 1.0 // Gradient
+alpha = 0.8 // Acceleration(km phps)
+u = 0.25 // Co-efficient of adhesion
+r = 44.5 // Train resistance(N/tonne)
+I = 10.0 // Rotational inertia(%)
+
+// Calculations
+W_e = W*(100+I)/100 // Accelerating weight of train(tonne)
+F_t = 277.8*W_e*alpha+W*r+98.1*W*G // Tractive effort(N)
+adhesive_weight = F_t/(u*9.81*1000) // Adhesive weight(tonnes)
+
+// Results
+disp("PART IV - EXAMPLE : 5.10 : SOLUTION :-")
+printf("\nMinimum adhesive weight of the locomotive = %.1f tonnes\n", adhesive_weight)
+printf("\nNOTE: ERROR: Train resistance is 44.5 N per tonne & not 45 N per tonne as mentioned in textbook problem statement")
diff --git a/3472/CH43/EX43.11/Example43_11.sce b/3472/CH43/EX43.11/Example43_11.sce
new file mode 100644
index 000000000..04866946a
--- /dev/null
+++ b/3472/CH43/EX43.11/Example43_11.sce
@@ -0,0 +1,34 @@
+// A Texbook on POWER SYSTEM ENGINEERING
+// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar
+// DHANPAT RAI & Co.
+// SECOND EDITION
+
+// PART IV : UTILIZATION AND TRACTION
+// CHAPTER 5: ELECTRIC TRACTION-SPEED TIME CURVES AND MECHANICS OF TRAIN MOVEMENT
+
+// EXAMPLE : 5.11 :
+// Page number 784
+clear ; clc ; close ; // Clear the work space and console
+
+// Given data
+W = 400.0 // Weight of train(tonne)
+G = 100.0/75 // Gradient
+alpha = 1.6 // Acceleration(km phps)
+r = 66.75 // Train resistance(N/tonne)
+I = 10.0 // Rotational inertia(%)
+V = 48.0 // Speed(kmph)
+n = 0.7 // Overall efficiency of equipment
+
+// Calculations
+W_e = W*(100+I)/100 // Accelerating weight of train(tonne)
+F_t = 277.8*W_e*alpha+W*r+98.1*W*G // Tractive effort(N)
+t = V/alpha // Time(sec)
+energy_a = F_t*V*t/(2*3600**2) // Energy usefully employed(kWh)
+G_r = 98.1*G+r // Force(N)
+work_tonne_km = G_r*1000 // Work done per tonne per km(Nw-m)
+energy_b = work_tonne_km/(n*3600) // Energy consumption(Wh per tonne-km)
+
+// Results
+disp("PART IV - EXAMPLE : 5.11 : SOLUTION :-")
+printf("\nCase(a): Energy usefully employed in attaining speed = %.2f kWh", energy_a)
+printf("\nCase(b): Specific energy consumption at steady state speed = %.1f Wh per tonne-km", energy_b)
diff --git a/3472/CH43/EX43.12/Example43_12.sce b/3472/CH43/EX43.12/Example43_12.sce
new file mode 100644
index 000000000..6daa0b040
--- /dev/null
+++ b/3472/CH43/EX43.12/Example43_12.sce
@@ -0,0 +1,27 @@
+// A Texbook on POWER SYSTEM ENGINEERING
+// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar
+// DHANPAT RAI & Co.
+// SECOND EDITION
+
+// PART IV : UTILIZATION AND TRACTION
+// CHAPTER 5: ELECTRIC TRACTION-SPEED TIME CURVES AND MECHANICS OF TRAIN MOVEMENT
+
+// EXAMPLE : 5.12 :
+// Page number 784-785
+clear ; clc ; close ; // Clear the work space and console
+
+// Given data
+W = 200.0 // Trailing weight(tonne)
+G = 1.0 // Gradient(%)
+alpha = 1.0 // Acceleration(km phps)
+u = 0.2 // Co-efficient of adhesion
+r = 50.0 // Train resistance(N/tonne)
+I = 10.0 // Rotational inertia(%)
+
+// Calculations
+W_L = ((277.8*(100+I)/100*alpha)+98.1*G+r)*W/(u*9.81*1000-((277.8*(100+I)/100*alpha)+98.1*G+r)) // Weight of locomotive(tonnes)
+
+// Results
+disp("PART IV - EXAMPLE : 5.12 : SOLUTION :-")
+printf("\nMinimum adhesive weight of a locomotive, W_L = %.1f tonnes\n", W_L)
+printf("\nNOTE: ERROR: Calculation mistake in textbook solution in calculating W_L")
diff --git a/3472/CH43/EX43.2/Example43_2.sce b/3472/CH43/EX43.2/Example43_2.sce
new file mode 100644
index 000000000..f7b0f6502
--- /dev/null
+++ b/3472/CH43/EX43.2/Example43_2.sce
@@ -0,0 +1,30 @@
+// A Texbook on POWER SYSTEM ENGINEERING
+// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar
+// DHANPAT RAI & Co.
+// SECOND EDITION
+
+// PART IV : UTILIZATION AND TRACTION
+// CHAPTER 5: ELECTRIC TRACTION-SPEED TIME CURVES AND MECHANICS OF TRAIN MOVEMENT
+
+// EXAMPLE : 5.2 :
+// Page number 778
+clear ; clc ; close ; // Clear the work space and console
+
+// Given data
+V_m = 65.0 // Maximum speed(kmph)
+t = 30.0 // Time of stop(sec)
+speed = 43.5 // Scheduled speed(kmph)
+alpha = 1.3 // Acceleration(km phps)
+D = 3.0 // Distance between 2 stops(km)
+
+// Calculations
+t_total = D*3600/speed // Total time of run including stop(sec)
+T = t_total-t // Actual time for run(sec)
+V_a = D/T*3600 // Average speed(kmph)
+beta = 1/((7200.0*D/V_m**2*((V_m/V_a)-1))-(1/alpha)) // Value of retardation(km phps)
+
+// Results
+disp("PART IV - EXAMPLE : 5.2 : SOLUTION :-")
+printf("\nValue of retardation, β = %.3f km phps\n", beta)
+printf("\nNOTE: Changes in the obtained answer from that of textbook is due to more precision here")
+printf("\n ERROR: β unit is km phps & not km phps as mentioned in textbook solution")
diff --git a/3472/CH43/EX43.3/Example43_3.sce b/3472/CH43/EX43.3/Example43_3.sce
new file mode 100644
index 000000000..b34a37915
--- /dev/null
+++ b/3472/CH43/EX43.3/Example43_3.sce
@@ -0,0 +1,29 @@
+// A Texbook on POWER SYSTEM ENGINEERING
+// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar
+// DHANPAT RAI & Co.
+// SECOND EDITION
+
+// PART IV : UTILIZATION AND TRACTION
+// CHAPTER 5: ELECTRIC TRACTION-SPEED TIME CURVES AND MECHANICS OF TRAIN MOVEMENT
+
+// EXAMPLE : 5.3 :
+// Page number 778-779
+clear ; clc ; close ; // Clear the work space and console
+
+// Given data
+speed = 25.0 // Scheduled speed(kmph)
+D = 800.0/1000 // Distance between 2 stations(km)
+t = 20.0 // Time of stop(sec)
+V_m_per = 20.0 // Maximum speed higher than(%)
+beta = 3.0 // Retardation(km phps)
+
+// Calculations
+t_total = D*3600/speed // Total time of run including stop(sec)
+T = t_total-t // Actual time for run(sec)
+V_a = D/T*3600 // Average speed(kmph)
+V_m = (100+V_m_per)*V_a/100 // Maximum speed(kmph)
+alpha = 1/((7200.0*D/V_m**2*((V_m/V_a)-1))-(1/beta)) // Value of acceleration(km phps)
+
+// Results
+disp("PART IV - EXAMPLE : 5.3 : SOLUTION :-")
+printf("\nRate of acceleration required to operate this service, α = %.2f km phps", alpha)
diff --git a/3472/CH43/EX43.4/Example43_4.sce b/3472/CH43/EX43.4/Example43_4.sce
new file mode 100644
index 000000000..99e20524e
--- /dev/null
+++ b/3472/CH43/EX43.4/Example43_4.sce
@@ -0,0 +1,32 @@
+// A Texbook on POWER SYSTEM ENGINEERING
+// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar
+// DHANPAT RAI & Co.
+// SECOND EDITION
+
+// PART IV : UTILIZATION AND TRACTION
+// CHAPTER 5: ELECTRIC TRACTION-SPEED TIME CURVES AND MECHANICS OF TRAIN MOVEMENT
+
+// EXAMPLE : 5.4 :
+// Page number 779
+clear ; clc ; close ; // Clear the work space and console
+
+// Given data
+D = 2.0 // Distance between 2 stations(km)
+V_a = 40.0 // Average speed(kmph)
+V_1 = 60.0 // Maximum speed limitation(kph)
+alpha = 2.0 // Acceleration(km phps)
+beta_c = 0.15 // Coasting retardation(km phps)
+beta = 3.0 // Braking retardation(km phps)
+
+// Calculations
+t_1 = V_1/alpha // Time for acceleration(sec)
+T = 3600*D/V_a // Actual time of run(sec)
+V_2 = (T-t_1-(V_1/beta_c))*beta*beta_c/(beta_c-beta) // Speed at the end of coasting period(kmph)
+t_2 = (V_1-V_2)/beta_c // Coasting period(sec)
+t_3 = V_2/beta // Braking period(sec)
+
+// Results
+disp("PART IV - EXAMPLE : 5.4 : SOLUTION :-")
+printf("\nDuration of acceleration, t_1 = %.f sec", t_1)
+printf("\nDuration of coasting, t_2 = %.f sec", t_2)
+printf("\nDuration of braking, t_3 = %.f sec", t_3)
diff --git a/3472/CH43/EX43.5/Example43_5.sce b/3472/CH43/EX43.5/Example43_5.sce
new file mode 100644
index 000000000..c20ad42d1
--- /dev/null
+++ b/3472/CH43/EX43.5/Example43_5.sce
@@ -0,0 +1,26 @@
+// A Texbook on POWER SYSTEM ENGINEERING
+// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar
+// DHANPAT RAI & Co.
+// SECOND EDITION
+
+// PART IV : UTILIZATION AND TRACTION
+// CHAPTER 5: ELECTRIC TRACTION-SPEED TIME CURVES AND MECHANICS OF TRAIN MOVEMENT
+
+// EXAMPLE : 5.5 :
+// Page number 781-782
+clear ; clc ; close ; // Clear the work space and console
+
+// Given data
+r = 1.0 // Tractive resistance(N/tonne)
+
+// Calculations
+tractive_res_i = 0.278*r // Tractive resistance(N/tonne) = Energy consumption(Wh/tonne-km)
+beta = 1/277.8 // Tractive resistance(N/tonne) = Retardation(km kmps/tonne)
+energy = 98.1*1000/3600 // 1% gradient = energy(Wh per tonne km)
+
+// Results
+disp("PART IV - EXAMPLE : 5.5 : SOLUTION :-")
+printf("\nCase(i) : Tractive resistance of 1 N per tonne = %.3f Wh per tonne-km", tractive_res_i)
+printf("\nCase(ii) : Tractive resistance of 1 N per tonne = %.5f km phps per tonne", beta)
+printf("\nCase(iii): 1 percent gradient = %.2f Wh per tonne km\n", energy)
+printf("\nNOTE: Slight change in the obtained answer from that of textbook is due to more precision here")
diff --git a/3472/CH43/EX43.6/Example43_6.sce b/3472/CH43/EX43.6/Example43_6.sce
new file mode 100644
index 000000000..7f09be3e1
--- /dev/null
+++ b/3472/CH43/EX43.6/Example43_6.sce
@@ -0,0 +1,36 @@
+// A Texbook on POWER SYSTEM ENGINEERING
+// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar
+// DHANPAT RAI & Co.
+// SECOND EDITION
+
+// PART IV : UTILIZATION AND TRACTION
+// CHAPTER 5: ELECTRIC TRACTION-SPEED TIME CURVES AND MECHANICS OF TRAIN MOVEMENT
+
+// EXAMPLE : 5.6 :
+// Page number 782
+clear ; clc ; close ; // Clear the work space and console
+
+// Given data
+W = 254.0 // Weight of motor-coach train(tonne)
+no = 4.0 // Number of motor
+t_1 = 20.0 // Time(sec)
+V_m = 40.25 // Maximum speed(kmph)
+G = 1.0 // Gradient(%)
+gamma = 3.5 // Gear ratio
+n = 0.95 // Gear efficiency
+D = 91.5/100 // Wheel diameter(m)
+r = 44.0 // Train resistance(N/tonne)
+I = 10.0 // Rotational inertia(%)
+
+// Calculations
+W_e = W*(100+I)/100 // Accelerating weight of train(tonne)
+alpha = V_m/t_1 // Acceleration(km phps)
+F_t = 277.8*W_e*alpha+W*r+98.1*W*G // Tractive effort(N)
+T = F_t*D/(2*n*gamma) // Torque developed(N-m)
+T_each = T/no // Torque developed by each motor(N-m)
+
+// Results
+disp("PART IV - EXAMPLE : 5.6 : SOLUTION :-")
+printf("\nTorque developed by each motor = %.f N-m\n", T_each)
+printf("\nNOTE: Changes in the obtained answer from that of textbook is due to more precision here & more approximation in textbook")
+printf("\n ERROR: W = 254 tonne, not 256 tonne as mentioned in textbook problem statement")
diff --git a/3472/CH43/EX43.7/Example43_7.sce b/3472/CH43/EX43.7/Example43_7.sce
new file mode 100644
index 000000000..2afb0db70
--- /dev/null
+++ b/3472/CH43/EX43.7/Example43_7.sce
@@ -0,0 +1,33 @@
+// A Texbook on POWER SYSTEM ENGINEERING
+// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar
+// DHANPAT RAI & Co.
+// SECOND EDITION
+
+// PART IV : UTILIZATION AND TRACTION
+// CHAPTER 5: ELECTRIC TRACTION-SPEED TIME CURVES AND MECHANICS OF TRAIN MOVEMENT
+
+// EXAMPLE : 5.7 :
+// Page number 782
+clear ; clc ; close ; // Clear the work space and console
+
+// Given data
+W = 203.0 // Weight of motor-coach train(tonne)
+no = 4.0 // Number of motors
+T = 5130.0 // Shaft torque(N-m)
+V_m = 42.0 // Maximum speed(kmph)
+G = 100.0/250 // Gradient
+gamma = 3.5 // Gear ratio
+n = 0.93 // Gear efficiency
+D = 91.5/100 // Wheel diameter(m)
+r = 45.0 // Train resistance(N/tonne)
+I = 10.0 // Rotational inertia(%)
+
+// Calculations
+W_e = W*(100+I)/100 // Accelerating weight of train(tonne)
+F_t = n*4*T*2*gamma/D // Tractive effort(N)
+alpha = (F_t-W*r-98.1*W*G)/(277.8*W_e) // Acceleration(km phps)
+t_1 = V_m/alpha // Time taken by train to attain speed(sec)
+
+// Results
+disp("PART IV - EXAMPLE : 5.7 : SOLUTION :-")
+printf("\nTime taken by train to attain speed, t_1 = %.1f sec", t_1)
diff --git a/3472/CH43/EX43.8/Ex43_8.png b/3472/CH43/EX43.8/Ex43_8.png
new file mode 100644
index 000000000..be2c075fb
--- /dev/null
+++ b/3472/CH43/EX43.8/Ex43_8.png
Binary files differ
diff --git a/3472/CH43/EX43.8/Example43_8.sce b/3472/CH43/EX43.8/Example43_8.sce
new file mode 100644
index 000000000..4e609fd39
--- /dev/null
+++ b/3472/CH43/EX43.8/Example43_8.sce
@@ -0,0 +1,44 @@
+// A Texbook on POWER SYSTEM ENGINEERING
+// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar
+// DHANPAT RAI & Co.
+// SECOND EDITION
+
+// PART IV : UTILIZATION AND TRACTION
+// CHAPTER 5: ELECTRIC TRACTION-SPEED TIME CURVES AND MECHANICS OF TRAIN MOVEMENT
+
+// EXAMPLE : 5.8 :
+// Page number 782-783
+clear ; clc ; close ; // Clear the work space and console
+
+// Given data
+V_a = 42.0 // Average speed of train(kmph)
+D = 1400.0/1000 // Distance(km)
+alpha = 1.7 // Acceleration(km phps)
+beta = 3.3 // Retardation(km phps)
+r = 50.0 // Tractive resistance(N/tonne)
+I = 10.0 // Rotational inertia(%)
+
+// Calculations
+T = D*3600/V_a // Time for run(sec)
+k = (alpha+beta)/(alpha*beta) // Constant
+V_m = (T/k)-((T/k)**2-(7200*D/k))**0.5 // Maximum speed over the run(kmph)
+t_1 = V_m/alpha // Time of acceleration(sec)
+t_3 = V_m/beta // Time(sec)
+t_2 = T-(t_1+t_3) // Time(sec)
+D_1 = D-(V_a*t_1/(2*3600)) // Distance(km)
+We_W = (100+I)/100 // W_e/W
+energy = (0.0107*V_m**2*We_W/D)+(0.278*r*D_1/D) // Energy consumption(Wh per tonne-km)
+a = gca() ;
+a.thickness = 2 // sets thickness of plot
+plot([0,t_1,t_1,(t_1+t_2),(t_1+t_2),(t_1+t_2+t_3)],[0,V_m,V_m,V_m,V_m,0]) // Plotting speed-time curve
+plot([t_1,t_1],[0,V_m],'r--')
+plot([t_1+t_2,t_1+t_2],[0,V_m],'r--')
+a.x_label.text = 'Time(seconds)' // labels x-axis
+a.y_label.text = 'Speed (km/h)' // labels y-axis
+xtitle("Fig E5.1 . Speed-time curve for the run")
+xset('thickness',2) // sets thickness of axes
+
+// Results
+disp("PART IV - EXAMPLE : 5.8 : SOLUTION :-")
+printf("\nSpeed-time curve for the run is shown in Figure E5.1")
+printf("\nEnergy consumption at the axles of train = %.1f Wh per tonne-km", energy)
diff --git a/3472/CH43/EX43.9/Example43_9.sce b/3472/CH43/EX43.9/Example43_9.sce
new file mode 100644
index 000000000..fa0ce06e7
--- /dev/null
+++ b/3472/CH43/EX43.9/Example43_9.sce
@@ -0,0 +1,41 @@
+// A Texbook on POWER SYSTEM ENGINEERING
+// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar
+// DHANPAT RAI & Co.
+// SECOND EDITION
+
+// PART IV : UTILIZATION AND TRACTION
+// CHAPTER 5: ELECTRIC TRACTION-SPEED TIME CURVES AND MECHANICS OF TRAIN MOVEMENT
+
+// EXAMPLE : 5.9 :
+// Page number 783
+clear ; clc ; close ; // Clear the work space and console
+
+// Given data
+V_A = 48.0 // Speed(kmph)
+t_1 = 24.0 // Time taken to accelerate from rest to speed(sec)
+t_2 = 69.0 // Coasting time(sec)
+r = 58.0 // Constant resistance(N/tonne)
+beta = 3.3 // Retardation(km phps)
+t_3 = 11.0 // Retardation time(sec)
+t_iii_a = 20.0 // Station stop time(sec)
+t_iii_b = 15.0 // Station stop time(sec)
+I = 10.0 // Rotational inertia(%)
+
+// Calculations
+alpha = V_A/t_1 // Acceleration(km phps)
+V_B = beta*t_3 // Speed at B(km phps)
+beta_c = (V_A-V_B)/t_2 // Retardation during coasting(km phps)
+distance_acc = 1.0/2*t_1*V_A/3600 // Distance covered during acceleration(km)
+distance_coasting = (V_A**2-V_B**2)/(2*beta_c*3600) // Distance covered during coasting(km)
+distance_braking = t_3*V_B/(3600*2) // Distance covered during braking(km)
+distance_total = distance_acc+distance_coasting+distance_braking // Total distance(km)
+speed_iii_a = distance_total*3600/(t_1+t_2+t_3+t_iii_a) // Scheduled speed with a stop of 20 sec(kmph)
+speed_iii_b = distance_total*3600/(t_1+t_2+t_3+t_iii_b) // Scheduled speed with a stop of 15 sec(kmph)
+
+// Results
+disp("PART IV - EXAMPLE : 5.9 : SOLUTION :-")
+printf("\nCase(i) : Acceleration, α = %.f km phps", alpha)
+printf("\nCase(ii) : Coasting retardation, β_c = %.2f km phps", beta_c)
+printf("\nCase(iii): Scheduled speed with a stop of 20 seconds = %.2f kmph", speed_iii_a)
+printf("\n Scheduled speed with a stop of 15 seconds = %.2f kmph\n", speed_iii_b)
+printf("\nNOTE: ERROR: Calculation mistakes in the textbook solution")