Answer
a) v=0.930m/s
b) v=2.83m/s
Work Step by Step
1) Split the acceleration into its components ($a_{r}$ and $a_{tan}$).
$a_{tan}$ will equal $cos(\theta)\times a$
$a_{r}$ will equal $sin(\theta)\times a$
According to the problem, $\theta=25^{\circ}$ and $a=1.05$.
Therefore,
$a_{tan}\approx 0.95162317638$
$a_{r}\approx 0.44374917482$
2) Use the formula for $a_{r}$ to find the velocity in this instant.
It is known that $a_{r}=\frac{v^{2}}{r}$ as $a_{r}$ is the centripetal acceleration.
Plug in the known values and solve for v.
$0.44374917482=\frac{v^{2}}{1.95}$
$0.86531089089=v^{2}$
$v=0.93022088285$
This is your velocity at this instant; when providing the answer, round to three sig figs.
3) Use the formula for $a_{tan}$ to find the velocity 2 seconds in the future.
$a_{tan}=\frac{\Delta v}{\Delta t}$
Plug in the values you know and solve for $\Delta v$
$0.95162317638 = \frac{\Delta v}{2}$
$1.90324635276 = \Delta v$
Because this is the change in velocity, you have to add it to the "initial" velocity, which is the velocity we found in step 2.
$v = 1.90324635276 + 0.93022088285$
$v = 2.83346723561$
This is your velocity 2 seconds into the future. Round to three sig figs.
