# A mass is able to move freely on an inclined, frictionless surface. If the angle of inclination...

## Question:

A mass is able to move freely on an inclined, frictionless surface. If the angle of inclination of 10{eq}^{\circ}{/eq}, and the mass is given an initial velocity {eq}v_0 = 1.2 \frac{m}{s}{/eq} up the incline,

a) How far up the incline will the mass move?

b) From the point it is released, how long will it take the mass to move up the inclined plane and fall back to its starting position?

## Newton's second law of motion and equations of motion:

According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting on the object and is inversely proportional to the mass of the object.

{eq}\displaystyle{ a\propto F_{net}\ \ \ \& \ \ \ a\propto \frac{1}{m}\\ or\\ a\propto \frac{F_{net}}{m}\\ or\\ \boxed{F_{net}= ma} } {/eq}

where;

• {eq}F_{net} {/eq} is the net force acting on the object
• {eq}m {/eq} is the mass of the object
• {eq}a {/eq} is the acceleration of the object

Equations of motions are a set of equations which relate the the various parameters associated with the motion of a uniformly accelerated object. These equations are;

{eq}\bullet v= u+at\\ \bullet v^2= u^2+2as\\ \bullet s= ut+\frac{1}{2}at^2 {/eq}

where;

• {eq}u\ \ \&\ \ v {/eq} are the initial and final velocities of the object
• {eq}s {/eq} is the distance moved by the object
• {eq}a {/eq} is the acceleration of the object
• {eq}t {/eq} is the time elapsed

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Given data:

• {eq}v_{i} = 1.2 \frac{m}{s} {/eq} is the initial velocity of the mass
• {eq}\theta = 10^{\circ} {/eq} is the angle of the inclined... Kinematic Equations: List & Example

from

Chapter 4 / Lesson 15
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What are kinematic equations of motion and their assumptions? Learn to derive the 5 kinematic equations and see applications of the kinematics formulas.