Question

A block of mass m is on 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 definition of velocity of the kinematics we find the answer for the time in which the velocity becomes zero is:

         t = 2 M / N

Kinematics studies the movement of bodies, establishes relationships between the position, velocity and acceleration of bodies

Velocity is defined as it varied from position with respect to time

        v = $\frac{dx}{dt}$

Where v is the velocity, x the position and t the time

They indicate the expression for the position  

         x (t) = M t - n t²

is requested when the velocity becomes zero, we look for the derivative

          v =  M - ½ N t

the point where the velocity is zero

          0 = M - ½ N t

         t = $\frac{2M}{N}$

In conclusion, using the definition of velocity from kinematics, we find the answer for the time in which the velocity becomes zero is:

         t = $\frac{2M}{N}$

Learn more about instantaneous velocity here:

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