The position of a 2 kg mass is given by \vec{r} ( t ) = [(3 m/s^2 ) t^2 - (7 m/s ) t + (2 m )]...
Question:
The position of a 2 kg mass is given by {eq}\vec{r} ( t ) = [(3 m/s^2 ) t^2 - (7 m/s ) t + (2 m )] \hat{i} + [( - 1 m/s^2 ) t^2 + (2 m/s ) t + (3 m )] \hat{j} {/eq} .
Give units in all your answers.
a) Determine the net force on the mass.
b) Determine the work done by the above force during the time interval t = 0 s to t = 3 s.
c) What is the change in the mass's speed between t = 0 and t = 3 s
d) Determine the instantaneous rate at which the above force does work on the mass (i.e., the instantaneous power) at t=3s.
Force and Work
Force (F) is given by the formula
{eq}F=ma {/eq}; where "m" is the mass and "a" is the acceleration.
while work "W" is given by the formula;
{eq}W = Fr {/eq}; where "r" is the displacement or change in position.
moreover, in terms of function,
given "r(t)" position as a function of time "t" ;
Velocity "v" is given by:
{eq}v = \frac{dr}{dt} {/eq};
Acceleration "a" is given by:
{eq}a = \frac{dr^2}{dt^2} {/eq};
Power "P" is given by:
{eq}P = Work/time= \frac {W}{t} {/eq}
Answer and Explanation: 1
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View this answerNow get the first and second partial derivative of the {eq}\vec{r} (t) {/eq}; for the velocity and acceleration.
Given
{eq}\vec{r} ( t ) = [(3...
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Chapter 18 / Lesson 5Read about the definition of resultant force and what it means. Discover the resultant force formula. Learn how to calculate resultant force using examples.