A particle executes the motion described by x(t)=x_0(1-e^ - );t 0… - Vidyadip

Question

A particle executes the motion described by $\text{x}(\text{t})=\text{x}_0(1-\text{e}^{-\gamma\text{t}});\text{t}\ge0,\text{x}_0>0.$
Find maximum and minimum values of x(t), v(t), a(t). Show that x(t) and a(t) increase with time and v(t) decreases with time.

✓

Answer

x(t) is minimum at $\text{t}=0\ \because\ \text{At t}=0,[\text{x}(\text{t})]_\text{min}=0$
x(t) is maximum at $\text{t}=\infty\ \because\ \text{At t}=\infty[\text{x}(\text{t})]_\text{max}=\text{e}-\gamma\text{t}=\infty$
v(t) is maximum at $\text{t}=0\ \because\ \text{At t}=0;\text{v}(0)=\text{x}_0\gamma$
v(t) is minimum at $\text{t}=\infty\ \because\ \text{At t}=\infty\text{ v}(\infty)=0$
a(t) is maximum at $\text{t}=\infty\ \because\ \text{At t}=\infty\text{ a}(\infty)=0$
a(t) is minimum at $\text{t}=0\because\text{At t}=0\ \text{a}(0)=-\text{x}_0\gamma^2$

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