The acceleration in ms-2 ofa body starting from restis given by
f(t)= 1/10te^0.1t
Determine the velocity of the body after 20 seconds
Do not know where to start
Remember:
$\displaystyle \ddot {x(t)} = \dot {v(t)} = a(t)$
Then:
$\displaystyle v = \int_{ }^{ } a(t)dt$
So we have:
$\displaystyle a(t) = \frac {t}{10}e^{\frac {t}{10}}$
We also know that $\displaystyle v(0) = 0$ since the body starts from rest.
Then:
$\displaystyle v(t) = \int_{ }^{ } \frac {t}{10}e^{\frac {t}{10}}$
This can be done by parts if you want. You get:
$\displaystyle v(t) = e^{t/10} (t-10) + c$.
Plug in your initial condition:
$\displaystyle 0 = (0 - 10) + c$.
Then,
$\displaystyle c = 10$.
Then,
$\displaystyle v(t) = e^{t/10} (t-10) + 10$.
If you want the velocity at t = 20, you have:
$\displaystyle v(20) = e^{20/10} (20-10) + 10 = (10e^{2}+10) \frac {m}{s}$