1. ## Stuck ? help

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

2. 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:

$\displaystyle v(t) = e^{t/10} (t-10) + c$.

$\displaystyle 0 = (0 - 10) + c$.

Then,

$\displaystyle c = 10$.

Then,

$\displaystyle v(t) = e^{t/10} (t-10) + 10$.

If you want the velocity at t = 20, you have:

$\displaystyle v(20) = e^{20/10} (20-10) + 10 = (10e^{2}+10) \frac {m}{s}$

3. thanks for your help,I am slowly getting to grips with it.