Physics, 09.09.2019 21:30 478978810

You drive on interstate 10 from san antonio to houston, half the time at 76 km/h and the other half at 119 km/h. on the way back you travel half the distance at 76 km/h and the other half at 119 km/h. what is your average speed (a) from san antonio to houston, (b) from houston back to san antonio, and (c) for the entire trip? (d) what is your average velocity for the entire trip?

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Answer from: jake2124

(a) 97.5km/h

(b) 97.5km/h

(d) 0km/h

Explanation:

Speed and velocity concepts: Velocity is a vector, but speed does not have a direction. Speed is a scalar quantity, it is the magnitude of the velocity.

What is the speed for:

(a) from San Antonio to Houston: Average speed=(76+119)/2=97.5km/h

(b) from Houston back to San Antonio: Average speed=(76+119)/2=97.5km/h

(d) What is your average velocity for the entire trip?

Velocity is the total distance divided the total time. For the entire trip the point of departure is the same at the point of arrival (San Antonio), so the vector distance travelled is zero, then the velocity for the entire trip is 0km/h

Answer from: Quest

answer; the correct answer is technician a; ///100%good luck

Answer from: Quest

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

$x(t)=ax(x-6)$

where $a$ is unknown. because the position is parabolic, there is symmetry about the midpoint at $t=3$ , and we know that

$x(3)=10\implies -9a=10\implies a=-\dfrac{10}9$

so that the position function is

$x(t)=-\dfrac{10}9x(x-6)$

which means the velocity is

$v(t)=\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac{20}9x+\dfrac{60}9$

then the total distance traveled is

$\displaystyle\int_{t=0}^{t=6}|v(t)|\,\mathrm dt=\left\{\int_{t-0}^{t=3}-\int_{t=3}^{t=6}\right\}v(t)\,\mathrm dt=20$

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at $x=0$ and ends at $x=0$ , so its displacement is 0.

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