• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Acceleration with position given

1. Homework Statement

The position of an object is given by r(t) = 4 cos(3t) i + 4 sin(3t) j (where distance is
in meters and time is in seconds). What is the magnitude of the object’s acceleration at
any given point in time?

2. Homework Equations

v=x/t a=v/t

3. The Attempt at a Solution
ok so i thoguht that since the x and y coordinates are 4 cos 3t and 4 sin 3t the hypotenuse would be 4 and then that would be the distance so then i solved for t by 4cos(3t)^2 + 4sin 3t^2=4^2 and i solved t to be 30 since sin of 3(30)=90 is 1 and cos of 90 is 0 then i used the 30 as my time and divided 4/30 to find the velocity and then use the velocity and plugged it in v/t and i get the wrong answer...where did i go wrong?
 

CompuChip

Science Advisor
Homework Helper
4,284
47
v = x / t only gives you the average (which is exact, whenever the acceleration is zero).

If you want the acceleration at any point in time, you need to differentiate.
v(t) = r'(t)
a(t) = v'(t) = r''(t)

where the prime denotes differentiation with respect to time.
 

Related Threads for: Acceleration with position given

Replies
4
Views
1K
Replies
2
Views
1K
Replies
5
Views
14K
Replies
15
Views
4K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top