The acceleration of the particle at t= 1.0s according to the position function, x is; a = 8.118 m/s²
The position of the particle is given as;
[tex]x = 15 {e}^{ - 2t} [/tex]
where t = time in seconds.
To find the acceleration; we must find the second derivative of x as follows;
[tex] \frac{dx}{dt} = - 30 {e}^{-2t} = velocity[/tex]
[tex] \frac{d²x}{dt²} = 60 {e}^{-2t} = acceleration[/tex]
The acceleration of the particle at t = 1.0s is therefore;
- [tex]acceleration = 60 {e}^{ - 2(1)} [/tex]
acceleration = 60 × 0.1353
Acceleration, a = 8.118m/s²
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