In [1]:

```
import math
#Initilization of Variables
u=2 #m/s #Initial velocity
v=5 #m/s #Final Velocity
t=4 #sec
#Calculations
a=(v-u)*t**-1 #m/s**2
#Result
print"Acceleration of the body is",round(a,2),"m/s**2"
```

In [2]:

```
import math
#Initilization of Variables
u=15 #m/s #Intital velocity
v=0 #m/s #Final velocity
t=5 #sec
#Calculations
#acceleration
a=u*t**-1 #m/s**2
#Distance
S=u*t-a*t**2*0.5
#Result
print"Retardation is",round(a,2),"m/s**2"
print"Distance travelled by the car is",round(S,2),"m"
```

In [3]:

```
import math
#Initilization of Variables
u=250 #m/s #Initial Velocity
v=0 #m/s #final Velocity
s1=0.40 #m #Distance
s2=0.20 #m #distance moved
#Calculations
#acceleration
a=u**2*(2*s1)**-1 #m/s**2
#velocity
v=(u**2-2*a*s2)**0.5 #m/s
#Result
print"Acceleration is",round(a,2),"m/s**2"
print"Velocity is",round(v,2),"m/s"
```

In [4]:

```
import math
#Initilization of Variables
L_AB=100 #m #Distance AB
L_BC=100 #m #distance BC
t1=10 #s #Time taken by car from A to B
t2=8 #s #Time taken by car from B to C
s=100 #m #Distance
L_AC=L_AB+L_BC #m
#Calculations
#From equation of distance we get value of velocity
#s=10*V_A+50*a ...........................1
#again using equation of distance we get
#L_AC=18*V_A+162*a .........................2
#After simplifying above equations we get equations like
#900=90*V_A+450*a ......................3
#1000=90*V_A+810*a ..............4
#Subtracting equations 3 by 4 we get
a=100*360**-1 #m/s**2
#Velocity of car A
V_A=(100-13.9)*10**-1 #m/s
#Velocity of car B
V_B=(L_BC-(a*t2**2*0.5))*t2**-1 #m/s
#Distance OA
s3=V_A**2*(2*a)**-1 #m/s
#Result
print"Acceleration of car is",round(a,2),"m/s**2"
print"Velocity of car A",round(V_A,2),"m/s"
print"Velocity of car B",round(V_B,2),"m/s"
print"distance of mark A from starting point is",round(s3,2),"m"
```

In [5]:

```
import math
#Initilization of Variables
u=0 #m/s #Initial velocity
a=2 #m/s**2 #Acceleration
u2=40 #m/s #Uniform velocity
#Calculations
#after simplifying Distance travelled we get
#t**2+20t+100=0 .................1
#Distance travelled by police party=40*t ..........2
#Equating equations 1 and 2 we get
#t**2-20*t+100
a=1
b=-20
c=100
X=b**-4*a*c
t=(-b+X**0.5)*(2*a)**-1 #s
#Result
print"TIme taken in which police van will overtake the car is",round(t,2),"s"
```

In [6]:

```
import math
#Initilization of Variables
v=10 #m/s #uniform Velocity
a=1 #m/s**2 #Uniform acceleration
u=10 #m/s #uniform velocity
#Calculations
#From distance equation and further simplifying we get
#S=(t**2+100-20*t) .................1
#again sub value in distance we get
#S=u*t ............2
#Equating two equations and further simplifying we get
#t**2-40*t+100=0
a=1
b=-40
c=100
X=b**2-4*a*c
t1=(-b+X**0.5)*(2*a)**-1 #s
t2=(-b-X**0.5)*(2*a)**-1 #s
#time required to catch smugglers car is
t3=(t1-10)
#Result
print"Time necesscary for the jeep to catch up with the smuggler's car is",round(t3,2),"s"
```

In [7]:

```
import math
#Initilization of Variables
u=0
a=4 #m/s**2
t1=7 #s
t2=6 #s
#Calculations
#Distance travelled in 7 seconds
S7=u*t1+0.5*a*t1**2 #m
#DistANCE TRAVELLED in 6 seconds
S6=u*t2+0.5*a*t2**2 #m
#Distance travelled in 7th second
S7_2=S7-S6
#Result
print"Distance travelled in 7th second is",round(S7_2,2),"s"
```

In [8]:

```
import math
#Initilization of Variables
S5=15 #m #Distance travelled for 5 th seconds
S10=25 #m #Distance travelled for 10 th seconds
n1=10
n2=5
#Calculations
#Equation for distance covered for nth seconds
#S=u+a*2**-1
#distance covered in 10 th second
#S10=u+a*2**-1*(2*n1-1) ...................1
#distance covered in 5 th second
#S5=u+a*2**-1*(2*n2-1) .........................2
#Subtracting equation 2 by 1 we get
a=10*(19-9)**-1*2
u=S5-9*2**-1*2
#Result
print"Initial Velocity of the body is",round(a,2),"m/s**2"
print"Acceleration of the body is",round(u,2),"m/s**2"
```

In [9]:

```
import math
#Initilization of Variables
h=90 #3mm Height of tower
h1=30 #m #Height at which both particles meet
S1=60 #m #Distance travelled by first particle
S2=30 #m
g2=-9.81 #m/s**2
#For Initial Velocity
u1=0
g=9.81 #m/s**2
#Calculations
#Time
t1=((S1*2)*g**-1)**0.5 #s
#For second particle
u2=(S2-0.5*g2*t1**2)*t1**-1
#Result
print"Velocity with which second particle projected is",round(u2,2),"m/s"
```

In [10]:

```
import math
#Initilization of Variables
h=800 #m #Height of aeroplane
U=166.67 #m/s
#First case
u1=0
h2=800 #m #Height of bomb when released
g=9.81 #m/s**2
#Calculations
#Time required to reach the ground
t=(h*2*(g)**-1)**0.5
#Horizontal distance travelled
S=U*t
#Result
print"Time required to reach the ground is",round(t,2),"s"
print"Horizontal distance travelled is",round(S,2),"m"
```

In [11]:

```
import math
#Initilization of Variables
u=0 #m/s #Initial velocity
g=9.81 #m/s**2 #acceleration due to gravity
#Calculations
#t1+t2=4 ...........1
#Depth of well after simplifying we get
#h=4.905*t1**2 ........2
#Time taken by sound to reach from bottom of well
#t2=4.905*t1**2*350**-1 #s ...............3
#Sub value in equation 1 and further simplifying we get
#4.905*t1**2+350*t1-1400=0
a=4.905
b=350
c=-1400
X=b**2-4*a*c
t1=(-b+X**0.5)*(2*a)**-1 #s
#Depth of well
h=4.905*t1**2 #m
#Result
print"Depth of well is",round(h,2),"m"
```

In [12]:

```
import math
#Initilization of Variables
u=19.6 #m/s #Initial velocity
h=24.5 #m #height of tower
g=9.80 #m/s**2 #acceleration de to gravity
#Calculations
#Max height of stone
h1=(u**2)*(2*g)**-1 #m
#Time for stone to move from A to C
t1=u*g**-1
#Time for stone to move from C to D
h2=h+h1 #m #Max height to which stone will rise
t2=((h2*4.9**-1))**0.5 #s
#Total time for stone to reach the ground
t=t1+t2 #s
#Result
print"Total time for stone to reach the ground is",round(t,2),"s"
print"Velocity of stone in downward travel is",round(u,2),"m/s"
print"Max height to which the stone will rise is",round(h2,2),"m"
```

In [13]:

```
import math
#Initilization of Variables
u=0 #Initial Velocity
t=5 #s #time taken by stone in striking the glass pane
g=9.81 #m/s**2
#Calculations
#velocity
v1=u+g*t #m/s
#Velocity lost in breaking stones
v2=20*100**-1*10
#Velocity of the stone after breaking the glass pane
v3=v1-v2 #m/s
#distance travelled in t2=1 s
t2=1 #s
s=v3*t2+0.5*g*t2**2 #m
#Result
print"Distance travelled by the stone in next second is",round(s,2),"m"
```

In [14]:

```
import math
#Initilization of Variables
u=0 #m/s
s=53.90 #m #Distance
g=9.80 #m/s**2 #Acceleration due to gravity
#Calculations
#Height
#After simplifying equation of distance we get
#h1=4.9*t**2 ..................................1
#Distance travelleed in (t-1) s
#After simplifying equation of distance we get
#h2=4.9(t-1)**2 ..................................2
#Distance travelled by object in last seconds
#h3=h-h2
#After substituting values in above equation we get
#h3=4.9(2*t-1)
#Equating h3 to s we get after simplifying
t=12*2**-1 #m/s
#height from which object falls
h1=4.9*t**2
#Result
print"height from which object falls is",round(t,2),"s"
print"Total time taken by object in falling is",round(h1,2),"m"
```

In [15]:

```
import math
#Initilization of Variables
g=9.80 #m/s**2
u=0 #m/s
#Calculations
#Distance travelled in time t after simplifiying
#h=4.9*t**2
#Distance travelled in (t-1)s
#h-h2=2*3**-1*h
#Substituting value we get equation as
#2*t**2-6*t+3=0
a=2
b=-6
c=3
X=b**2-4*a*c
t=(-b+X**0.5)*(2*a)**-1 #s
t2=(-b-X**0.5)*(2*a)**-1 #s
#Height of tower
h=4.9*t**2
#Result
print"Height of tower is",round(h,2),"m"
```

In [16]:

```
import math
#Initilization of Variables
u1=30 #m/s #Initial Vlocity of 1st object
u2=40 #m/s #Initial Velocity of2nd object
#Calculations
#For the first object
#After simplifying we get
#h1=30*t-4.905*t**2 ................1
#For second object
##After simplifying we get
#h2=40*(t-4)-4.905(t-4)**2 ...........2
#Equating equations 1 and 2 and further simplify we get
t=238.48*49.24**-1 #s
#height
h=30*t-4.905*t**2 #m
#Result
print"Time whrn the two objects will meet each other is",round(t,2),"s"
print"Height from the earth at which the two objects will meet is",round(h,2),"m"
```

In [17]:

```
import math
#Initilization of Variables
h=100 #m #Height of tower
u1=0 #Initial velocity of 1st particle
S2=30 #m #Distace travelled by 2nd particle
S1=70 #m #Distance travelled by 1st paerticle
g=9.81 #m/s**2
#Calculations
#time of particle 1
t=(S1*(g*2**-1)**-1)**0.5 #s
#Initial velocity
u=((S2+(g*2**-1)*t**2)*t**-1) #m/s
#Result
print"Velocity with which the second particle is projected upward is",round(u,2),"m/s"
```

In [18]:

```
import math
#Initilization of Variables
n=5 #Rate of drops
u=0 #Initial Velocity
v=3 #m/s #Final Velocity
g=9.81 #m/s**2
t=3*9.81**-1 #s
#Calculations
#Vertical Distance
Sb=u*t+0.5*g*t**2 #m
#time taken by drop A
t2=3*9.81**-1-0.2 #s
#Vertical Distance travelled from mouth of faucet by drop A
Sa=u*t2+0.5*g*t2**2 #m
#Vertical Separation between drops A and B
S=Sb-Sa #m
#Result
print"Vertical separation between two drops is",round(S,3),"m"
```

In [19]:

```
import math
#Initilization of Variables
u=0 #m/s**2 #Initial Velocity
#S=(x+20) #m #distance
g=9.81 #m/s**2
#Calculations
#Distance travelled by Body in time t
#x=0.5*g*t**2 .................................1
#Distance travelled by body in time (t+0.4)s
#S2=0.5(t**2+0.**t+0.16) ........................2
#Subtracting equation 2 from 1 we get
t=3.92*0.80**-1
#Distance travelled by Body in time t is given by
x=0.5*g*t**2 #m
#Result
print"Distance travelled by Body in time t is",round(x,2),"m"
```

In [20]:

```
import math
#Initilization of Variables
#Equation of displacement
#s=t**3+3*t**2+4*t+5
#Calculations
#After differentiating displacement equation we get velocity at t=0
#At
t=0
v=3*t**2+6*t+4 #m/s
#Velocity at t=4 seconds
t2=4
v2=3*t2**2+6*t2+4 #m/s
#After differentiating w.r.to t we get equation of acceleration as
#a=6*t+6
#at t=0
t3=0
a=6*t3+6 #m/s**2
#at t=4
t4=4
a2=6*t4+6 #m/s**2
#Result
print"Velocity at start of 4seconds is",round(v,2),"m/s"
print"Velocity after 4seconds is",round(v2,2),"m/s"
print"Acceleration at start is",round(a,2),"m/s**2"
print"Acceleration after four seconds is",round(a2,2),"m/s**2"
```

In [21]:

```
import math
#Initilization of Variables
#Equation of particle motion
#s=18*t+3*t**2-2*t**3
#Calculations
#After differentiating w.r.to t to above equation we get
#6*t**2-6*t-18
#at
t=0
#Velocity
v=6*t**2+6*t+18
#After differentiating above equation again we get equation of acceleration
#at
t2=0
a=6-12*t2
#After differentiating equation of velocity we get value of
t2=6*12**-1
vmax=18+6*t2-6*t2**2 #m/s
#Result
print"Velocity at start is",round(v,2),"m/s"
print"Acceleration at start is",round(a,2),"m/s**2"
print"Time when it reaches max velocity is",round(t2,2),"s"
print"MAx velocity of particle is",round(vmax,2),"m/s"
```

In [22]:

```
import math
#Initilization of Variables
#a=-**s**-2 #m/s**2
t=1 #s #time
s=4 #m #Distance
v=2 #m/s #Velocity
t2=2 #s #time
#Calculations
#Acceleration equation
#a=v*(dv*ds**-1)
#After sub values and further simplifying and integrating the obtained equation we get
#v**2=8*s**-1+C1 ...................1
#Sub equation in above equations we get
C1=v**2*2**-1-8*s**-1
#Sub value in equation 1 and furter simplifying and integrating obtained equation we get
#2*3**-1*s**(3*2**_1)=4*t+c2
#Sub values
C2=2*3**-1*s**(3*2**-1)-4*t
#Sub value of C2 and further sub values we get
s=14**(2*3**-1)
#Acceleration
a=8*s**-2 #m/s**2
#Result
print"Acceleration when t=2 is",round(a,4),"m/s**2"
```

In [23]:

```
import math
#Initilization of Variables
#a=4*t**2-2
t1=0
s1=-2 #m
t2=2 #s
s2=-20 #m
t3=4 #s
#Calculations
#a=4*t**2-2
#After integrating above equations we getand further simplifying we get equation of distance as
#s=t**4*3**-1-t**2+C1*t+C2
C2=s1-t1**4*3**-1
#s=t**4*3**-1-t**2+C1*t-2 ...............3
#Now after sub in equation and further simplifying the equation we get
C1=(s2-t2**4*3**-1+t2**2+2)*t2**-1
#Sub in above equation 3 we get
#when t=4
t4=4
s3=t4**4*3**-1-t4**2+C1*t4-2
#Result
print"Position of particle when t=4 s is",round(s3,2),"s"
```

In [24]:

```
import math
#Initilization of Variables
#v=2*t**3-t**2-2*t**2-2*t+4
t=2 #s
s=10 #m
t2=6 #s
#Calculations
#acceleration
a=6*t2**2-2*t2-2 #m/s**2
#Displacement when t=6s
#After integrating and further simplifying the equation of velocity we get equation of displacement as
#s=2*t**4*4**-1-t**3*3**-1-t**2+4*t+C ...............1
#After sub values we get
C=s-(2*t**4*4**-1-t**3*3**-1-t**2+4*t)
#Sub value of C in equation
s2=2*t2**4*4**-1-t2**3*3**-1-t2**2+4*t2+C #m
#Result
print"Acceleration is",round(a,2),"m/s**2"
print"Displacement of particle when t=6 s is",round(s2,2),"m"
```

In [57]:

```
import math
#Initilization of Variables
#a=2-3*t
t=5 #s
t2=10 #s
v=20 #m/s #velocity
s=85 #m #displacement
#Calculations
#Acceleration at start when t=0
a=2-3*t
#Equation of acceleration after integrating and further simplifying we get
C1=v-(2*t-3*t**2*2**-1)
#After substituting in equation and further simplifying we get
#At t3=0
t3=0
v=2*t3-3*t3**2*2**-1+C1
#After differentiating equation of velocity and integrating it we get equation of displacement as
#s=t**2-3*t**3*6**-1+47.5*t+C2
C2=s-(t2**2-3*t2**3*6**-1+47.5*t2)
#sub value of C2 in above equation we get
s2=t3**2-3*t3**3*6**-1+47.5*t3+C2
#Sub v=0 in equation 3 we get an duaqratic equation as
#3*t**2-4*t-95=0
a=3
b=-4
c=-95
X=b**2-4*a*c
t4=(-b+(X**0.5))*(2*a)**-1 #s
#Sub value of t4 in equation of displacement and we get
s3=t4**2-3*t4**3*6**-1+47.5*t4+C2
#Result
print"Acceleration from origin at start of observation is",round(a,2),"m/s**2"
print"Velocity from origin at start of observation is",round(v,2),"m/s**2"
print"distance from origin at start of observationis",round(s2,2),"m"
print"Time after start of observation is",round(t4,2),"s"
print"Distance from origin is",round(s3,2),"m"
```