Velocity of a Car The velocity of a car (in feet per second) t sec after starting from rest is given by the function f(t) = 11 t (0 ≤ t ≤ 30). Find the car's position, s(t), at any time t. Assume that s(0) = 0. s(t) =

Using an integral, it is found that the car's position, at any time t, is given by:

The velocity of the car is modeled by the following function:

The position is the integrative of the velocity, hence:

In which the constant of integration K is the initial position. Since the initial position is , the constant is , and hence, the car's position, at any time t, is given by:

A similar problem is given at link

Step-by-step explanation:

Velocity is defined as the rate of change in displacement of a body. It is expressed mathematically as v = change in displacement/time

v(t) = ds(t)/dt

ds(t) = v(t)dt

integrating both sides;

s(t) =  

Given the velocity function f(t) = 11t, the car's position (displacement) is expressed as s(t) =

s(t) = 11t²/2 + C

at the initial point, s(0) = 0 i.e when t = 0, s(t) = 0. The resulting equation becomes;

0 = 11(0)²/2+ C

0 = 0+C

C = 0

To find the car's position, s(t), we will substitute C = 0 into the equayion above;

s(t) = 11t²/2 + 0

s(t) = 11t²/2

Hence s(t) = 11t²/2  is the required position of the car in terms of t.

answer:

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step-by-step explanation: