Question

A block of mass m is on the surface of negligible friction that is inclined at an angle of θ above the horizontal. The block is initially moving up the incline, and its position x as a function of time t is given by the equation x(t)=Mt−Nt2, where M has units of ms and N has units of ms2. The value of t when the block comes to rest is most nearly

Answer 1

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.

$v = \frac{d\ x(t)}{dt} = M - 2Nt\\\\v =0\\\\M-2Nt = 0\\\\2Nt = M\\\\t = \frac{M}{2N} = \frac{m/s}{2 \ m/s^2} = \frac{s}{2} = (\frac{1}{2} ) \ s\\\\t = 0.5 \ s$

Thus, the value of t  when the block comes to rest is most nearly 0.5 s.

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