Answer
(a) The crate travels $17.6~m$ down the incline in $2.50~s$
(b) The crate's speed after $2.50~s$ is $14.1~m/s$
Work Step by Step
(a) We can find the crate's acceleration:
$mg~sin~\theta = ma$
$a = g~sin~\theta$
$a = (9.80~m/s^2)~sin~35.0^{\circ}$
$a = 5.62~m/s^2$
We can find the distance the crate travels down the incline in $2.50~s$:
$d = \frac{1}{2}at^2$
$d = \frac{1}{2}(5.62~m/s^2)(2.50~s)^2$
$d = 17.6~m$
The crate travels $17.6~m$ down the incline in $2.50~s$
(b) We can find he speed after $2.50~s$:
$v_f = v_0+at$
$v_f = 0+(5.62~m/s^2)(2.50~s)$
$v_f = 14.1~m/s$
The crate's speed after $2.50~s$ is $14.1~m/s$.
