A particle moves linearly from the point (−2, 4) to (10, 0) in 4 seconds. Find parametric equations to describe this motion.

Step 1 The given points are (x1, y1)=(−2, 4); (x2, y2)=(10, 0) So the slope is given by: m=y2−y1x2−x1=0−410−(−2)=−13 Step 3 The Parametric equations can written as: x=x1+(y2−y14)t y=4+(0−44)t y=4−t Hence the parametric equations are x=−2+3andy=4−t.

Solved: "A particle moves linearly from the point (−2,..."

High School
Calculus and Analysis
Calculus 2
Parametric equations

varaderiyw

Answered question

2021-12-04

A particle moves linearly from the point

(- 2, 4)

(10, 0)

in 4 seconds. Find parametric equations to describe this motion.

Answer & Explanation

Harr1957

Beginner2021-12-05Added 18 answers

Step 1
The given points are $(x_{1}, y_{1}) = (- 2, 4); (x_{2}, y_{2}) = (10, 0)$
So the slope is given by:
$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{0 - 4}{10 - (- 2)} = \frac{- 1}{3}$
Step 3
The Parametric equations can written as:
$x = x_{1} + (\frac{y_{2} - y_{1}}{4}) t$
$y = 4 + (\frac{0 - 4}{4}) t$
$y = 4 - t$
Hence the parametric equations are $x = - 2 + 3 and y = 4 - t .$

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