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Kinematics answered problems

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Kinematics Answered Problems
Problem 1: Acceleration and Displacement
The velocity of a particle undergoing rectilinear motion is 

. Find the acceleration and
the displacement at t = 10s, if  at .
Solution:







  











  

 


When t=10 sec,



Problem 2: Displacement and acceleration
The displacement of a body is given by 
 
 , where s is displacement in m and t is time in
seconds. Determine the displacement of the body, when its velocity changes from 20 m/s to 60 m/s.
Also, find the acceleration after 5s.
Displacement of the body when v = 20 m/s

 
 



 
 

 

 

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
 


 
 

 
 
Displacement of the body when v = 60 m/s

 
 



 
 

 

 

 


 
 

 
 
Acceleration after 5 seconds





 


  

 

Problem 3: Velocity and Acceleration
A car moves along a straight line whose equation of motion is given by  
 
where s is
displacement in m and t is time in seconds. Calculate the (a) velocity and acceleration at the start, (b)
acceleration when velocity is equal to zero.

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Kinematics Answered Problems Problem 1: Acceleration and Displacement The velocity of a particle undergoing rectilinear motion is 𝑣 = 4𝑡 3 + 20𝑡 𝑚 . 𝑠 Find the acceleration and the displacement at t = 10s, if 𝑠𝑜 = 0 at 𝑡 = 0𝑠. Solution: 𝑣 = 4𝑡 3 + 20𝑡 𝑎= 𝑚 𝑠 𝑑𝑣 = 12𝑡 2 + 20, 𝑤ℎ𝑒𝑛 𝑡 = 10 𝑠𝑒𝑐 𝑑𝑡 𝑎 = 12(102 ) + 20 = 120 𝑚 𝑠2 𝑑𝑠 𝑚 = 4𝑡 3 + 20𝑡 𝑑𝑡 𝑠 𝑣= 𝑠 𝑠 ∫ 𝑑𝑠 = ∫ (4𝑡 3 + 20𝑡 0 0 𝑚 )𝑑𝑡 𝑠 𝑠 𝑡 𝑠 ⎢ = (𝑡 4 + 10𝑡 2 )⎢ 0 0 𝑠 − 0 = (𝑡 4 + 10𝑡 2 ) − (04 + 10(0)2 ) 𝑠 = (𝑡 4 + 10𝑡 2 ) When t=10 sec, 𝑠 = (104 + 10(10)2 ) = 11000 𝑚 Problem 2: Displacement and acceleration The displacement of a body is given by 𝑠 = 4𝑡 3 + 𝑡 2 + 6, where s is displacement in m and t is time in seconds. Determine the displacement of the body, when its velocity changes from 20 m/s to 60 m/s. Also, find the acceleration after 5s. Displacement of the body when v = 20 m/s 𝑠 = 4𝑡 3 + 𝑡 2 + 6 𝑣= 𝑑𝑠 (4𝑡 3 + 𝑡 2 + 6) 𝑑𝑡 𝑣 = 12𝑡 2 + 2𝑡 = 20 12𝑡 2 + 2𝑡 − 20 = 0 6𝑡 2 + 𝑡 − 10 𝑡 = 1.21 𝑠𝑒𝑐. 𝑠 = 4𝑡 3 + 𝑡 2 + 6 𝑠 = 4𝑡(1.21)3 + (1.21)2 + 6 = 14.55 𝑚 Displacement of the body when v = 60 m/s 𝑠 = 4𝑡 3 + 𝑡 2 + 6 𝑣= 𝑑𝑠 (4𝑡 3 + 𝑡 2 + 6) 𝑑𝑡 𝑣 = 12𝑡 2 + 2𝑡 = 60 12𝑡 2 + 2𝑡 − 60 = 0 ...
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