Instantaneous acceleration from coordinates?

[jalessandrom]

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

a_ins = lim_t->0 dv / dt
= lim_t->0 d²x / dt²

The Attempt at a Solution

My attempt went as follows:

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

a for y-coordinate:
a_ins = lim_t->2 d²(7 + 2t + t³) / dt²
= lim_t->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.

 

[jalessandrom]

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

 

[AlephNumbers]

Good job. Welcome to PF, by the way.

 

[AlephNumbers]

= 4 x 2 = 8 m/s2

Why did you multiply by two?

 

[Ahmadhuss]

so what's the answer?

 

[PeroK]

This thread is over five years old.