# Homework Help: Instantaneous acceleration from coordinates?

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1. Apr 21, 2015

### jalessandrom

1. The problem statement, all variables and given/known data
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?

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

2. Relevant equations
ains = limt->0 dv / dt
= limt->0 d2x / dt2

3. 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.

2. Apr 21, 2015

### jalessandrom

Solved thanks! derived a for the y-coordinate incorrectly.

3. Apr 21, 2015

### AlephNumbers

Good job. Welcome to PF, by the way.

4. Apr 21, 2015

### AlephNumbers

Why did you multiply by two?