Question
The velocity of a car (in feet per second) $t$ sec after starting from rest is given by the function$$f(t)=2 \sqrt{t} \quad(0 \leq t \leq 30)$$Find the car's position, $s(t),$ at any time $t .$ Assume that $s(0)=0$
Step 1
We know that the position function is the integral of the velocity function. So, we need to find the integral of $f(t)$. Show more…
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The velocity of a car (in feet per second) $t$ sec after starting from rest is given by the function $$f(t)=2 \sqrt{t} \quad(0 \leq t \leq 30)$$ Find the car's position, $s(t),$ at any time $t$. Assume that $s(0)=0$.
Integration
Antiderivatives and the Rules of Integration
A car slows down with an acceleration of $a(t)=-15 \mathrm{ft} / \mathrm{s}^{2} .$ Assume $v(0)=60 \mathrm{ft} / \mathrm{s}, s(0)=0,$ and $t$ is measured in seconds. a. Determine the position function, for $t \geq 0$ b. How far does the car travel in the time it takes to come to rest?
Applications of Integration
Velocity and Net Change
Let $f(t)$ be the velocity in meters/second of a car at time $t$ in seconds. Give an integral for the change in the position of the car (a) Over the time interval $0 \leq t \leq 60$. (b) In terms of time $T$ in minutes, over the same time interval.
Integration by Substitution
Transcript
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