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The velocity of a particle traveling along a straight line is $v=\left(3 t^{2}-6 t\right) \mathrm{ft} / \mathrm{s},$ where $t$ is in seconds. If $s=4 \mathrm{ft}$ when $t=0,$ determine the position of the particle when $t=4$ s. What is the total distance traveled during the time interval $t=0$ to $t=4 \mathrm{s} ?$ Also, what is the acceleration when $t=2 \mathrm{s} ?$

a. $s(4)=20 \mathrm{ft}$.b. Distance traveled $=24 f t$.c. $a(2)=6 f t / s^{2}$

Physics 101 Mechanics

Chapter 12

Kinematics of a Particle

Motion Along a Straight Line

Newton's Laws of Motion

Applying Newton's Laws

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Well, position is a function of time. Could be regiones integral 40 times. DT So, uh, this into girl is equal to three d squared minus 60 times DT. Since we equals Treaty Square minus 60 and solving this integral, our position is a function of time Musical two D, Q Minus free T square. Let's see where sees a constant well, it Time t is equal to zero. Uh, position is zero Q minus three to CDO square place scene and therefore si is equal to four. So C is equal to four, right? Since ah c equals all right position in Time T is equal to zero, So seize equal to four and further, like music rollup um, we have position is a function of time is equal to a cube minus three t square less four feet and position when time physical four seconds is equal to forgive Minus three into four square this fuller musical to 20 peach right, So we have that's not is equal to four feet and s one is equal to 20 feet and some office not And this one is equal to 24 feet. No, let's find out acts relation we don't which is, um TV divided Fine TT eyes equal to x relation of the function of time which is equal to 60 minus six feet or second squared. So x relation when time physical two seconds His six into two mine six Matiz ical to six beat were second square.

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