For the given equation of speed v 5 + 3t, write down the equation of displacement for the first 7 with movements.

Given:

v (t) = 5 + 3 * t – the equation of the dependence of the body’s speed on time;

t = 7 seconds – time span.

It is required to compose the equation of motion of the body and find its path S (meter) in time t.

Since it is not specified in the problem statement, we assume that the initial coordinate of the body is zero.

Let’s find the initial velocity of the body at t = 0:

v0 = 5 + 3 * t = 5 + 3 * 0 = 5 m / s.

Let’s find the acceleration of the body:

a = v (t) ‘= (5 + 3 * t)’ = 3 m / s2.

Then the equation of body motion will be:

x (t) = x0 + v0 * t + a * t ^ 2/2 = 5 * t + 3 * t2 / 2.

Let, passed in 7 seconds, be:

S = 5 * t + 3 * t ^ 2/2 = 5 * 7 + 3 * 7 ^ 2/2 = 35 + 3 * 49/2 =

= 35 + 73.5 = 108.5 meters.

Answer: the equation of body motion x (t) = 5 * t + 3 * t ^ 2/2, in 7 seconds the body will travel 108.5 meters.