The dependence of the coordinates of the body on time is described by the equation x = 3 + 13t + 7t2.

The dependence of the coordinates of the body on time is described by the equation x = 3 + 13t + 7t2. What is the acceleration of the body? Write down the equation of speed versus time for this body.

As you know, if the dependence of the x coordinate of the body on the time t is described by the equation x = x (t) = x0 + v0 * t + a * t² / 2, where x0 is the coordinate of the point of the body at the time of the beginning of observations, v0 is the initial velocity of the body, a is the magnitude of the acceleration of the body, then the motion of this body is uniformly accelerated motion. In the case of uniformly accelerated motion, the speed v of the body’s motion depends on time t linearly: v = v (t) = v0 + a * t, and the acceleration is a constant value. In our case, x = x (t) = 3 + 13 * t + 7 * t². Therefore, the acceleration of the body can be found from the equality: a / 2 = 7. We have: a = 7 * 2 = 14. The equation of speed versus time for this body has the form: v = v (t) = 13 + 14 * t.