 # Equations of Motion Questions

In physics, equations of motion describe the behaviour of a body or system in terms of its movement as a function of time. The equation of motion defines the nature of a body as a group of mathematical functions using dynamic variables. Such variables are generally time and spatial coordinates. In some cases, it may incorporate momentum components. The generalised coordinates are the most usual choices. It can be any appropriate variable, typical of the physical system. These functions are based on Euclidean geometry in classical mechanics. On the other hand, it is substituted by curved spaces in relativity.

Fundamentally, there are dual descriptions of motion: kinematics and dynamics. Kinematics is a simple approach to motion that only deals with variables derived from objects’ position and time. In the case of constant acceleration, these equations of motion are generally mentioned as the SUVAT equations. It was formed from the definitions of kinematic constraints: displacement ‘s’, initial velocity ‘u’, final velocity ‘u’, acceleration ‘a’, and time ‘t’. On the other hand, dynamics stands for complex motion scenarios. Dynamic quantities like energy and forces are taken into account. In this case, occasionally, the term dynamics directly refers to the differential equations that the object or system satisfies, and sometimes to the results of those equations.

## Equations of Motion

In the scenario of motion with constant or uniform acceleration (system with equal variation in velocity in an equal time interval), there are five basic equations of motion. Displacement(s), acceleration(a), and velocity (initial and final) are the quantities of the equation that control the motion of a particle. The standard equations of motion can only be used when a body’s acceleration is constant, and its movement is in a straight line. The equations of motion are:

$$\begin{array}{l}v = u + at\end{array}$$

$$\begin{array}{l}s = ut + \frac{1}{2}at^{2} \end{array}$$

$$\begin{array}{l}v^{2} = u^{2} + 2as\end{array}$$

Here,

$$\begin{array}{l}u\textup{ is the initial velocity,}\end{array}$$
$$\begin{array}{l}v\textup{ is the final velocity,}\end{array}$$
$$\begin{array}{l}a\textup{ is the acceleration,}\end{array}$$
$$\begin{array}{l}t\textup{ is the time.}\end{array}$$

## Important Equations of Motion Questions with Answers

1) What is the importance of equations of motion?

Equations of motion are used to describe the nature of a body’s motion. The equation of motion defines the nature of a body as a group of mathematical functions using dynamic variables. Such variables are generally time and spatial coordinates. In some cases, it may incorporate momentum components. The generalised coordinates are the most usual choices. It can be any appropriate variable, typical of the physical system. These functions are based on Euclidean geometry in classical mechanics. On the other hand, it is substituted by curved spaces in relativity.

2) What are the two descriptions of motion?

Kinematics and dynamics are the two fundamental descriptions of motion.

Kinematics is a simple approach to motion that only deals with variables derived from objects’ position and time. In the case of constant acceleration, these equations of motion are generally mentioned as the SUVAT equations. It was formed from the definitions of kinematic constraints: displacement ‘s’, initial velocity ‘u’, final velocity ‘u’, acceleration ‘a’, and time ‘t’. On the other hand, dynamics stands for complex motion scenarios. Dynamic quantities like energy and forces are taken into account. In this case, occasionally, the term dynamics directly refers to the differential equations that the object or system satisfies and sometimes to the results of those equations.

3) What are the variables that control the motion of an object with constant or uniform acceleration?

Displacement(s), acceleration(a), and velocity (initial and final) are the quantities of the equation that control the motion of an object.

4) What are the classic five equations of motion?

Five equations of motion are:

$$\begin{array}{l}v = u + at\end{array}$$
$$\begin{array}{l}s = ut + \frac{1}{2}at^{2} \end{array}$$
$$\begin{array}{l}v^{2} = u^{2} + 2as\end{array}$$

$$\begin{array}{l}s = \frac{1}{2}(u + v)t\end{array}$$
$$\begin{array}{l}s = vt – \frac{1}{2} at^2 \end{array}$$

Here,

$$\begin{array}{l}u\textup{ is the initial velocity,}\end{array}$$
$$\begin{array}{l}v\textup{ is the final velocity,}\end{array}$$
$$\begin{array}{l}a\textup{ is the acceleration,}\end{array}$$
$$\begin{array}{l}t\textup{ is the time.}\end{array}$$

5) Give the equations of the displacement.

The equations of the displacement are:

$$\begin{array}{l}s = ut + \frac{1}{2}at^{2} \end{array}$$
$$\begin{array}{l}s = \frac{1}{2}(u + v)t\end{array}$$
$$\begin{array}{l}s = vt – \frac{1}{2} at^2 \end{array}$$

$$\begin{array}{l}v^{2} = u^{2} + 2as\end{array}$$

6) Give the equations of the initial velocity.
The equations of the initial velocity are:

$$\begin{array}{l}v = u + at\end{array}$$

$$\begin{array}{l}v^{2} = u^{2} + 2as\end{array}$$

$$\begin{array}{l}s = \frac{1}{2}(u + v)t\end{array}$$

7) Give the equations of final velocity.
The equations of final velocity are:

$$\begin{array}{l}v = u + at\end{array}$$

$$\begin{array}{l}v^{2} = u^{2} + 2as\end{array}$$

$$\begin{array}{l}s = \frac{1}{2}(u + v)t\end{array}$$

$$\begin{array}{l}s = vt – \frac{1}{2} at^2 \end{array}$$

8) Give the equations of time.
The equations of time are:

$$\begin{array}{l}v = u + at\end{array}$$

$$\begin{array}{l}s = ut + \frac{1}{2}at^{2} \end{array}$$

$$\begin{array}{l}s = \frac{1}{2}(u + v)t\end{array}$$

$$\begin{array}{l}s = vt – \frac{1}{2} at^2 \end{array}$$

9) Give the equation that shows the relationship between the initial velocity, final velocity, acceleration, and time.
The equation is:

$$\begin{array}{l}v = u + at\end{array}$$

10) Give the equation that shows the relationship between displacement, initial velocity, time, and acceleration.
The equation is:

$$\begin{array}{l}s = ut + \frac{1}{2}at^{2} \end{array}$$

11) Give the equation that shows the relationship between displacement, initial velocity, final velocity, and time.
The equation is:

$$\begin{array}{l}s = \frac{1}{2}(u + v)t\end{array}$$

12) Give the equation that shows the relationship between final velocity, initial velocity, acceleration and displacement.
The equation is:

$$\begin{array}{l}v^{2} = u^{2} + 2as\end{array}$$

13) Give the equation that shows the relationship between displacement, final velocity, time, and acceleration.
The equation is:

$$\begin{array}{l}s = vt – \frac{1}{2} at^2 \end{array}$$

## Practice Questions

1) What are the SUVAT equations?

2) What is meant by dynamics?

3) What is meant by kinematics?

4) What is the relationship between acceleration and displacement?

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