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Laws of Motion

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Question : 24 of 40
Marks: +1, -0
Figure shows the position-time graph of a body of mass 0.04 kg. Suggest a suitable physical context for this motion. What is the time between two consecutive impulses received by the body? What is the magnitude of each impulse?
Solution:  
Here, m=0.04 kgm = 0.04 \, \text{kg}. Position time graph shows that the particle movesfrom x=0x = 0 at O to x=2x = 2cm at A in 2 s.
As x-t graph is a straight line, the motion is with a constant velocity
u=(2−0) cm(2−0) su = \frac{(2-0) \, \text{cm}}{(2-0) \, \text{s}} =1 cm s−1=10−2 m s−1= 1 \, \text{cm} \, \text{s}^{-1} = 10^{-2} \, \text{m} \, \text{s}^{-1}
From x=2x = 2cm at A, particle goes to x=0x = 0 at B in 2 s.
As AB is a straight line, motion is with constant velocity
v=(0−2) cm(4−2) sv = \frac{(0-2) \, \text{cm}}{(4-2) \, \text{s}} =−1 cm s−1=−10−2 cm s−1= -1 \, \text{cm} \, \text{s}^{-1} = -10^{-2} \, \text{cm} \, \text{s}^{-1}
Negative sign indicates the reversal of direction of motion. This is being repeated. We can visualise a ball moving between two walls located at x = 0 and x = 2 cm, getting rebounded repeatedly on striking against each wall. On every collision with a wall, linear momentum of the ball changes.
Therefore, the ball receives impulse after every two seconds.
Magnitude of impulse = total change in linear momentum
=mu−mv=m(u−v)= m u - m v = m(u - v)
=0.04[10−2−(−10−2)]= 0.04 [10^{-2} - (-10^{-2})]
=0.04(10−2+10−2)= 0.04 (10^{-2} + 10^{-2})
=0.08×10−2=8×10−4 kg m s−1= 0.08 \times 10^{-2} = 8 \times 10^{-4} \, \text{kg} \, \text{m} \, \text{s}^{-1}
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