Question

a particle moves in the xy plane according to the equation x=4t^2+4t+5 and y=t^3+12t+3 at t=1s, the acceleration of the particle is​

Answer 1

Explanation:

d^2 y/dt^2 at t=1 will be 6

Answer 2

Answer:

The acceleration of the particle is 10m/$s^{2}$

Explanation:

Given:-

X= 4$t^{2}$ + 4t + 5       Y = $t^{3}$ + 12t + 3        at  t = 1sec

velocity along x- axis $v_{x}$ = $\frac{dx}{dt}$

$v_{x}$ = $\frac{d(4t^{2}+4t+5) }{dt}$

$v_{x}$ = 8t + 4 m/s

acceleration along x-axis

$a_{x}$ = $\frac{d(v_{x}) }{dt}$

$a_{x}$ = $\frac{d(8t + 4)}{dt}$

$a_{x}$ = 8m/$s^{2}$

velocity along y-axis $v_{y}$ = $\frac{dy}{dt}$

$v_{y}$ = $\frac{d(t^{3}+12t +3) }{dt}$

$v_{y}$ = 3$t^{2}$ + 12 m/s

acceleration along y-axis

$a_{y}$ = $\frac{d(v_{y}) }{dt}$

$a_{y}$ = $\frac{d(3t^{2} + 12) }{dt}$

$a_{y}$ = 6t

$a_{y}$ = 6m/$s^{2}$

The acceleration of the particle is given by :

a =$\sqrt{a_{x}i + a_{y}j }$

mod of a = $\sqrt{a_{x}^{2} +a_{y}^{2} }$

a =$\sqrt{8^{2}+6^{2} }$

a =$\sqrt{64 + 36}$

a =$\sqrt{100}$

a = 10 m/$s^{2}$