Instantaneous acceleration from coordinates?

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Homework Help Overview

The problem involves determining the instantaneous acceleration of an automobile given its position coordinates as functions of time. The coordinates are defined as x(t) = 5 + 3t + 2t² and y(t) = 7 + 2t + t³, with the task focused on evaluating the acceleration at t = 2 seconds.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the calculation of acceleration for both x and y coordinates, with one participant questioning the multiplication by two in the acceleration calculation. There is also a mention of an incorrect derivation for the y-coordinate's acceleration.

Discussion Status

The discussion includes attempts to clarify the calculations involved in finding the instantaneous acceleration. Some participants have provided feedback and corrections, while others have expressed confusion about specific steps taken in the calculations. There is no explicit consensus on the final answer, but guidance has been offered regarding the derivation errors.

Contextual Notes

Participants are working within the constraints of homework rules, which may limit the extent of assistance provided. The original poster seeks advice on their calculations without revealing complete solutions.

jalessandrom
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Homework Statement


The coordinate of an automobile in meters is x(t) = 5 + 3t + 2t2 and y(t) = 7 + 2t + t3, where t is in seconds. What is the instant acceleration of the car at time t = 2 s?

ANSWERS:
A. 10.2 m/s2
B. 9.5 m/s2
C. 7.9 m/s2
D. 15.0 m/s2
E. 12.6 m/s2

Homework Equations


ains = limt->0 dv / dt
= limt->0 d2x / dt2

The Attempt at a Solution


My attempt went as follows:

a for x-coordinate:
ains = limt->2 d2(5 + 3t + 2t2) / dt2
= limt->2 4 m/s2
= 4 x 2 = 8 m/s2

a for y-coordinate:
ains = limt->2 d2(7 + 2t + t3) / dt2
= limt->2 3 m/s2
=3 x 2 = 6 m/s2

For a:
√82 + 62 = 10 m/s2

Just wondering what I am doing incorrectly, any advice would be appreciated.
 
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Solved thanks! derived a for the y-coordinate incorrectly.
 
Good job. Welcome to PF, by the way.
 
jalessandrom said:
= 4 x 2 = 8 m/s2

Why did you multiply by two?
 
so what's the answer?
 
This thread is over five years old.
 

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