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Llana [10]
3 years ago
15

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) =
Mathematics
1 answer:
pochemuha3 years ago
6 0

Answer:

<h2>s(t) = 11t²/2 </h2>

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) =  \int\limits v(t)dt

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

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.

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