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