The movement of a material point is given by the equation x = 4t-0.05t ^ 2. Determine the moment in time at which the speed

The movement of a material point is given by the equation x = 4t-0.05t ^ 2. Determine the moment in time at which the speed of the point is zero. Find coordinates and acceleration at this moment.

1) Speed of a point (derivative of the function of motion of a material point):

x ‘= V = (4t – 0.05t ^ 2)’ = 4 – 2 * 0.05t = 4 – 0.1t m / s.

2) The moment in time when the speed of a point is zero, V = 0 m / s.

0 = 4 – 0.1t.

0.1t = 4.

t = 4 / 0.1 = 40 s.

3) The coordinates of the point at the moment t = 40 s:

x (40) = 4 * 40 – 0.05 * 40 ^ 2 = 160 – 80 = 80 m.

4) Acceleration of a point (second-order derivative of the point motion function):

x ” = V ‘= a = (4t – 0.05t ^ 2)’ ‘= (4 – 0.1t)’ = -0.1 m / s2 (motion is equally slow).