The position of a particle for t> 0 is given by 7 (t) = ((31²) Î + (−6.8 t³) ƒ + (−5 t¯²) k) m. Assume all quantities are correct to 2 significant figures. (a) What is the velocity as a function of time t? Think: In terms of derivatives, how is velocity related to the postion vector when expressed as a function of time? v(t)=( (b) What is the acceleration as a function of time 't'? Think: In terms of derivatives, how is acceleration related to the velocity vector when expressed as a function of time? a(t): = (c) What is the particle's velocity at t = 1.7 s? Enter to 2 significant figures v(t = 1.7 s) = ( + i+ m S (d) What is its speed at t = 0.6 s and t = 3.4 s? Think: Speed at any instant is the magntitude of instantaneous velocity m m S

Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter1: Getting Started
Section: Chapter Questions
Problem 18PQ: Acceleration a has the dimensions of length per time squared, speed v has the dimensions of length...
icon
Related questions
icon
Concept explainers
Topic Video
Question

PLEASE ANSWER ALL PARTS AND I WILL RATE HIGHLY ! *17

1. The position of a particle for t > 0 is given by
7 (t) = ((3t²) Î + (−6.8 t³) ƒ + (−5 t¯²) k) m.
Assume all quantities are correct to 2 significant figures.
(a) What is the velocity as a function of time t?
Think: In terms of derivatives, how is velocity related to the postion vector when expressed as a
function of time?
v(t) = (
a(t) = (
i+
✓i+
(c) What is the particle's velocity at t = 1.7 s?
Enter to 2 significant figures
v(t = 1.7 s) = (
|v(t =3.4 s)|=|
(b) What is the acceleration as a function of time 't'?
Think: In terms of derivatives, how is acceleration related to the velocity vector when expressed as a
function of time?
'+
✓
✓i+
(d) What is its speed at t = 0.6 s and t = 3.4 s?
Think: Speed at any instant is the magntitude of instantaneous velocity
Enter to 2 significant figures
|v(t = 0.6 s) | =
m
S
m
i+
✓j+
k)
m
k)
|
S
m
s²
ES
m
Transcribed Image Text:1. The position of a particle for t > 0 is given by 7 (t) = ((3t²) Î + (−6.8 t³) ƒ + (−5 t¯²) k) m. Assume all quantities are correct to 2 significant figures. (a) What is the velocity as a function of time t? Think: In terms of derivatives, how is velocity related to the postion vector when expressed as a function of time? v(t) = ( a(t) = ( i+ ✓i+ (c) What is the particle's velocity at t = 1.7 s? Enter to 2 significant figures v(t = 1.7 s) = ( |v(t =3.4 s)|=| (b) What is the acceleration as a function of time 't'? Think: In terms of derivatives, how is acceleration related to the velocity vector when expressed as a function of time? '+ ✓ ✓i+ (d) What is its speed at t = 0.6 s and t = 3.4 s? Think: Speed at any instant is the magntitude of instantaneous velocity Enter to 2 significant figures |v(t = 0.6 s) | = m S m i+ ✓j+ k) m k) | S m s² ES m
(e) What is the average velocity between t = 0.6 s and t = 3.4 s?
Enter to 2 significant figures
Think: What is the formula for the average velocity?
V = (
✓i+
+
k)
m
S
Transcribed Image Text:(e) What is the average velocity between t = 0.6 s and t = 3.4 s? Enter to 2 significant figures Think: What is the formula for the average velocity? V = ( ✓i+ + k) m S
Expert Solution
steps

Step by step

Solved in 6 steps with 9 images

Blurred answer
Knowledge Booster
Projectile motion
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Physics for Scientists and Engineers: Foundations…
Physics for Scientists and Engineers: Foundations…
Physics
ISBN:
9781133939146
Author:
Katz, Debora M.
Publisher:
Cengage Learning
University Physics Volume 1
University Physics Volume 1
Physics
ISBN:
9781938168277
Author:
William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:
OpenStax - Rice University