The equation for the coordinate of a material point is: x = 20 + 5t + t ^ 2. Describe the nature of the movement

The equation for the coordinate of a material point is: x = 20 + 5t + t ^ 2. Describe the nature of the movement, find the initial speed, the movement of the car in 10 s. Make up the equation of speed

This equation corresponds to the uniformly accelerated motion of a material point. The velocity equation is obtained by differentiating the coordinate equation with respect to time:

v = (20 + 5t + t ^ 2) ‘= 5 + 2t.

Hence the initial speed:

v0 = 5 + 2 * 0 = 5.

Moving s10 in 10 s is obtained by subtracting the x (0) coordinate from the x (10) coordinate:

s10 = x (10) – x (0) = 20 + 5 * 10 + 10 ^ 2 – 20 – 5 * 0 – 0 ^ 2 = 20 + 50 + 100 – 20 = 150.

Answer: the movement is uniformly accelerated, v = 5 + 2t, v0 = 5, s10 = 150.