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Sagot :
The value of t when the block comes to rest is most nearly 0.5 s.
The given equation of motion;
x(t) = Mt - Nt²
The given units of M and N are;
M ------> m/s
N -------> m/s²
When the block comes to rest the final velocity of the block will be zero.
Velocity is change in displacement per change in time.
[tex]v = \frac{d\ x(t)}{dt} = M - 2Nt\\\\v =0\\\\M-2Nt = 0\\\\2Nt = M\\\\t = \frac{M}{2N} = \frac{m/s}{2 \ m/s^2} = \frac{s}{2} = (\frac{1}{2} ) \ s\\\\t = 0.5 \ s[/tex]
Thus, the value of t when the block comes to rest is most nearly 0.5 s.
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