Answer:
The acceleration of the particle at any time t
[tex]a = 4\ m/s^{2}[/tex]
Step-by-step explanation:
Given:
The position of a particle moving in a straight line at any time t is.
[tex]x(t) = 2t^{2} + 6t + 5[/tex]
The velocity of the particle [tex]v = \frac{d(x)}{d(t)}[/tex]
[tex]v = \frac{d}{d(t)}(2t^{2} + 6t + 5)[/tex]
[tex]v= 2\times 2t + 6[/tex]
[tex]v= 4t + 6[/tex]
So the velocity of the particle [tex]v= (4t + 6)\ m/s[/tex]
The acceleration of the particle [tex]a = \frac{d(v)}{d(t)}[/tex]
[tex]a = \frac{d}{d(t)}(4t + 6)[/tex]
[tex]a = 4\ m/s^{2}[/tex]
In this condition the acceleration does not depending upon the time, so the acceleration is constant
Therefore the acceleration of the particle at any time t [tex]a = 4\ m/s^{2}[/tex]
