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Asked by arushkumar6607 | 16 Jun, 2022, 08:46: AM
Expert Answer
when  time is greater than zero and less than 4 , displacement is linearly increasing
 
let x = a + b t  ................................(1)
 
at t = 0 , x = 0 , hence we get  a = 0
 
at t = 0 , x = 4 , hence we get b = 1
 
hence during the interval t=0 to t=4 , displacement x = t
 
---------------------------
 
During the interval t=4 to t = 10 , displacement x remains constant as 4
 
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when  time is greater than 10 and less than 14 , displacement is linearly decreasing
 
let in this time interval ,  x = a + b t  ................................(2)
 
at t = 10 , x = 4 , hence we get  a + 10 t = 4  ............... (3)
 
at t = 14 , x = -4 , hence we get a + 14 t  = -4  .................(4)
 
By solving eqn.(3) and eqn.(4) , we get a = 24 and b = -2
 
hence during the interval t=10 to t=14 , displacement x = 24-2t
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when  time is greater than 14 and less than 18 , displacement is linearly increasing
 
let in this time interval ,  x = a + b t  ................................(5)
 
at t = 14 , x = -4 , hence we get  a + 14 t = -4  ............... (6)
 
at t = 18 , x = 0 , hence we get a + 18 t  = 0  .................(7)
 
By solving eqn.(6) and eqn.(7) , we get a = -18 and b = 1
 
hence during the interval t=10 to t=14 , displacement x = t-18
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hence given displacement as a function of time t is
 
Displacement equation
  time interval
x = t 0 < t < 4
x = 4 4 < t < 10
x = 24 - 2t 10 < t < 14
x = t - 18 14 < t < 18

 
 
From above expressions we get displacement at required time as given in table
 
t x
1 1
2 2
4 4
6 4
11 2
13 -2
16 -2
-------------------------------------------------------------------------
 
Velocity dx/dt  as a function of time t is
 
dx/dt  = 1  , when  0 < t < 4
 
dx/dt = 0 , when 4 < t < 10
 
dx/dt = - 2 , when 10 < t < 14
 
dx/dt =  1 , when 14 < t < 18
 
From above expressions we get velocity at required time as given in table
 
 
t dx/dt
1 1
2 1
4 0
6 0
11 -2
13 -2
16 1
 
 
--------------------------------------------------------
since velocity is constant in all time intervals, acceleration d2x/dt2   is given as
 
d2x/dt2   = 0   , when 0 < t < 18
 
   
 
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