Equations of Motion for Beginners: Simple Solutions

Engineering
Thread starter Just Myry
Start date Nov 14, 2020
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Equations of motion Motion

In summary, an equation of motion is a mathematical representation of an object's position, velocity, and acceleration over time, describing how its motion changes due to external forces. The three equations of motion are the position, velocity, and acceleration equations, which can be solved by plugging in values for at least three of the four variables. Displacement and distance are different concepts, with displacement being a vector quantity and distance being a scalar quantity. Equations of motion are important in science as they allow for predictions and understanding of an object's motion, and are used in various fields such as physics, engineering, and astronomy.

Nov 14, 2020

Just Myry

Homework Statement: The acceleration of a particle is defined by the relation a = kt2. (a) Knowing that v = -8 m/s when t = 0 and that v = +8 m/s when t = 2 s, determine the constant k. (b) Write the equations of motion (define position as a function of time, x(t)), knowing also that x = 0 when t = 2 s.

Relevant Equations: a=kt2
v1=8 m/s
t1=0
v2= + 8 m/s
tw= 2 s

I am beginner. Can anybody do that? I need solution. Thanks so much!

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Nov 14, 2020

anuttarasammyak

Gold Member

Have you already learned calculus ?
[tex]a=\frac{dv}{dt}=kt^2[/tex]
[tex]v(0)=-8[/tex]
[tex]v(2)=8[/tex]

Last edited: Nov 14, 2020

1. What are the basic equations of motion?

The basic equations of motion are:

1. Velocity (v) = Displacement (s) / Time (t)

2. Acceleration (a) = Change in Velocity (Δv) / Time (t)

3. Displacement (s) = Initial Velocity (u) * Time (t) + 1/2 * Acceleration (a) * Time (t)^2

4. Final Velocity (v) = Initial Velocity (u) + Acceleration (a) * Time (t)

5. Displacement (s) = 1/2 * (Initial Velocity (u) + Final Velocity (v)) * Time (t)

2. What is the difference between speed and velocity?

Speed is a scalar quantity that only measures the magnitude of an object's motion. Velocity is a vector quantity that measures both the magnitude and direction of an object's motion.

3. How do I calculate acceleration?

Acceleration can be calculated by dividing the change in velocity (Δv) by the change in time (Δt): Acceleration (a) = Δv / Δt. Alternatively, it can be calculated using the equation a = (v-u)/t, where v is the final velocity, u is the initial velocity, and t is the time taken.

4. What is the difference between displacement and distance?

Displacement is a vector quantity that measures the distance and direction of an object's change in position. Distance is a scalar quantity that only measures the total length of the path traveled by an object.

5. How do I use equations of motion to solve problems?

To solve problems using equations of motion, you first need to identify the known and unknown variables. Then, choose the appropriate equation and rearrange it to solve for the unknown variable. Make sure to pay attention to units and use the correct formula for the given situation.