Answer
(a) $0.431 m/s^{2}$
(b) $21.6 m$
(c) $4.31 m/s$
Work Step by Step
(a) From Newton's Second Law of Motion, we can use $∑F ⃗ = ma ⃗ $ to find the acceleration.
Re-arrange the equation to solve for a. Since the Force and acceleration are acting upon the x-axis, we can re-write the equation as $a_{x} = F_{x}/m$.
Therefore, $a_{x} = F_{x}/m = (14.0 N) / (32.5 kg) = 0.431 m/s^{2}$.
(b) We can use the kinematic equation for constant acceleration: $x - x_{0} = v_{0x}t + \frac{1}{2}a_{x}t^{2} $. This particluar equation is used because it deals with $x$, $t$, and $a_{x}$, and from these variables we can solve for displacement x in this problem.
Since both the initial velocity $v_{0x}$ and initial displacement $x_{0}$ are 0, the equation can be re-written as $x = \frac{1}{2}at^{2}$.
Therefore, at $t = 10.0 s$, $x = \frac{1}{2}at^{2} = \frac{1}{2}(0.43m/s^{2})(10.0 s)^{2} = 21.6m$
(c) The kinematic equation $v_{x} = v_{0x} + a_{x}t$ for constant acceleration can be used to solve for $v_{x}$. Since the initial velocity is 0, the equation can be re-written as $v_{x} = a_{x}t$.
Therefore at $t = 10.0s$, $v_{x} = a_{x}t = (0.43 m/s^{2})(10.0s) = 4.31 m/s$.
