Chapter 03:Uniform Accelerated Motion

Ex3.1:pg-97

In [1]:
  import math #Example 3_1


  #To find the balls instantaneous velocity and Average Velocity
d1=8.6     #units in meters
t1=0.86     #units in sec
vp=d1/t1     #units in meters/sec
print "The Instantaneous Velocity at P Vp=",round(vp)," meters/sec\n"
  #The ball stops at position Q Hence vp=0 met/sec
vq=0    #units in meters/sec
print "The Instantaneous Velocity at Q Vq=",round(vq,10)," meters/sec\n"
d2=-10.2     #units in meters
t2=1.02     #units in sec
vn=d2/t2     #units in meters/sec
print "The Instantaneous Velocity at N Vn=",round(vn)," meters/sec\n"
d3=20     #units in meters
t3=2.0     #units in sec
vAQ=d3/t3     #units in meters/sec
print "The Average Velocity between A and Q is VAQ=",round(vAQ)," meters/sec\n"
d4=0     #units in meters
t4=4.0     #units in sec
vAM=d4/t4     #units in meters/sec
print "The Average Velocity between A and M is VAM=",round(vAM,10)," meters/sec\n"

The Instantaneous Velocity at P Vp= 10.0  meters/sec

The Instantaneous Velocity at Q Vq= 0.0  meters/sec

The Instantaneous Velocity at N Vn= -10.0  meters/sec

The Average Velocity between A and Q is VAQ= 10.0  meters/sec

The Average Velocity between A and M is VAM= 0.0  meters/sec

Ex3.2:pg-98

In [2]:
  import math #Example 3_2


  #To calculate the Acceleration
v1=20.0    #units in meters/sec
v2=15.0    #units in meters/sec
t1=0    #units in sec
t2=0.5    #units in sec
c_v=v2-v1     #units in meters/sec
c_t=t2-t1     #units in sec
acceleration=c_v/c_t    #units in meters/sec**2
print "Acceleration a=",round(acceleration,2)," meters/sec**2"

Acceleration a= -10.0  meters/sec**2

Ex3.3:pg-98

In [3]:
  import math #Example 3_3


  #To find acceleration and the distance it travels in time
vf=5.0    #units in meters/sec
v0=0   #units in meters/sec
t=10.0    #units in sec
a=(vf-v0)/t     #units in meters/sec**2
v_1=(vf+v0)/2     #unis in meters/sec
x=v_1*t    #units in meters
print "Acceleration is a=",round(a,1)," meters/sec\n"
print "Distance travelled is x=",round(x)," meters"

Acceleration is a= 0.5  meters/sec

Distance travelled is x= 25.0  meters

Ex3.4:pg-99

In [4]:
  import math #Example 3_4


  #To find acceleration and time taken to stop
v0=5.0    #units in meters/sec
vf=0     #units in meters/sec
v_1=(v0+vf)/2    #units in meters/sec
x=20.0     #units in meters
t=x/v_1     #units in sec
a=(vf-v0)/t    #units in meters/sec**2
print "Acceleration is a=",round(a,3)," meters/sec**2\n"
print "Time taken to stop t=",round(t)," sec"

Acceleration is a= -0.625  meters/sec**2

Time taken to stop t= 8.0  sec

Ex3.5:pg-100

In [6]:
  import math #Example 3_5

  
  #To calculate the speed and time to cover
a=4.0    #units in meters/sec**2
x=20.0     #units in meters
vf=math.sqrt(a*x*2)    #units in meters/sec
t=vf/a    #units in sec
print "Speed vf=",round(vf,2)," meters/sec\n"
print "Time taken T=",round(t,2)," sec"

Speed vf= 12.65  meters/sec

Time taken T= 3.16  sec

Ex3.6:pg-112

In [7]:
  import math #Example 3_6
 
 
  #To find the time taken by a car to travel
x=98.0    #uniys in meters
a=4.0     #units in meters/sec**2
t=math.sqrt((2*x)/a)    #units in sec
print "Time taken by a car to travel is T=",round(t)," sec"

Time taken by a car to travel is T= 7.0  sec

Ex3.7:pg-112

In [8]:
  import math #Example 3_7
   
  #To calculate the time taken to travel
v0=16.7    #units in meters/sec
a=1.5    #units in meters/sec**2
x=70    #units in meters
t=-((-v0)+math.sqrt(v0**2-(4*(a/2)*x)))/(2*(a/2))    #units in sec
print "Time taken to travel T=",round(t,1)," sec"

Time taken to travel T= 5.6  sec

Ex3.8:pg-114

In [9]:
  import math #Example 3_8
 
  
  #To calculate the acceleration
vf=30.0    #units in meters/sec
v0=0    #units in meters/sec
t=9.0    #units in sec
a=(vf-v0)/t    #units in meters/sec**2
a=a*(1/1000.0)*(3600.0/1)*(3600.0/1)    #units in km/h**2
print "Acceleration a=",round(a)," km/h**2"

Acceleration a= 43200.0  km/h**2

Ex3.9:pg-114

In [14]:
  import math #Example 3_9
 
  
  #To find how above the water is the bridge
v0=0    #units in meters/sec
t=3.0    #units in sec
a=-9.8     #units in meters/sec**2
y=(v0*t)+(0.5*a*t**2)    #units in meters
print "The bridge is y=",round(y)," meters above the water"

The bridge is y= -44.0  meters above the water

Ex3.10:pg-115

In [10]:
  import math #Example 3_10
 
  #To find out how high does it goes and its speed and how long will it be in air 
vf=0    #units in meters/sec
v0=15    #units in meters/sec
a=-9.8    #units in meters/sec**2
y=(vf**2-v0**2)/(2*a)     #units in meters
print "Distance it travels is y=",round(y,1)," meters\n"
vf=-math.sqrt(2*a*-y)    #units in meters/sec
print "The speed is vf=",round(vf)," meters/sec\n"
t=vf/(0.5*a)    #units in sec
print "Time taken is T=",round(t,2)," sec"

Distance it travels is y= 11.5  meters

The speed is vf= -15.0  meters/sec

Time taken is T= 3.06  sec

Ex3.11:pg-116

In [11]:
  import math #Example 3_11
 
  
  #To find out how fast a ball must be thrown
a=9.8    #unita in meters/sec**2
t=3    #units in sec
v=(0.5*a*t**2)/t
print "The speed by which the ball has to be thrown is v=",round(v,1)," meters/sec"

The speed by which the ball has to be thrown is v= 14.7  meters/sec

Ex3.12:pg-117

In [12]:
  import math #Example 3_12
 
 
#To find out where the ball will hit the ground
#Horizontal
y=2    #units in meters
a=9.8    #units in meters/sec**2
t=math.sqrt(y/(0.5*a))    #units in sec
v=15    #units in meters/sec
x=v*t    #units in sec
print "The ball hits the ground at x=",round(x,2)," meters"

The ball hits the ground at x= 9.58  meters

Ex3.13:pg-118

In [13]:
  import math #Example 3_13
 
  
  #To find out at what height above ground does it hit wall and is it still going up befor it hits or down
v_1=24.0    #units in meters/sec
x=15.0     #units in meters
t=x/v_1     #units in sec
v0=18    #units in meters/sec
a=-9.8    #units in meters/sec**2
y=(v0*t)+(0.5*a*t**2)    #units in meters
print "The arrow hits y=",round(y,1)," meters above the straight point\n"
v=v0+(a*t)     #units in meters/sec
print "The Vertical componet of velocity is v=",round(v,1)," meters/sec\n"
print "As V is Positive the arrow is in its way up\n"
vtotal=math.sqrt(v**2+v_1**2)     #units in meters/sec
print "The magnitude of velocity is vtotal=",round(vtotal,1)," meters/sec"

The arrow hits y= 9.3  meters above the straight point

The Vertical componet of velocity is v= 11.9  meters/sec

As V is Positive the arrow is in its way up

The magnitude of velocity is vtotal= 26.8  meters/sec