Physics, 26.12.2019 02:31 NoodlesYT

Acar travels on a long, straight highway at a constant speed of 30 m/s when it passes a stationary police motorcycle. as the car passes the motorcycle, the motorcycle accelerates at a constant rate of 10 m/s2 to try to catch up to the car. how far will the motorcycle travel before it catches up to the car?

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Answer from: madisonrendler1787

180 m

Explanation:

Given:

Uniform speed of the car, U = 30 m/s

Uniform acceleration of the motorcycle = 10 m/s²

For the motorcycle to catch up with the car, the distance traveled must be the same.

For the car;

Distance = Speed × Time

⇒ d = u × t

d = 30 × t

d = 30t ......(1)

For the motorcycle;

The stationary police motorcycle has initial speed, u = 0

From equation of motion;

$d = ut + \frac{1}{2}at^{2}$

but u = 0

$d = \frac{1}{2}at^{2}$

$d = \frac{1}{2}10t^{2}$

$d = 5t^{2}$ .....(2)

Equating equation (1) and (2)

30t = 5t²

$\frac{t^{2}}{t} = \frac{30}{5}$

t = 6 seconds

Substituting t = 6 s into equation (2)

d = 5(6)²

d = 5 × 36

d = 180 m

The motorcycle must travel 180 m before it catches up to the car

Answer from: Quest

Look it up you feel me

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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Acar travels on a long, straight highway at a constant speed of 30 m/s when it passes a stationary p...