# Kinematic Equations: A Guide for HSC Physics Students

This topic is part of the HSC Physics course under the section *Motion in a Straight Line*.

### HSC Physics Syllabus

**use mathematical modelling and graphs, selected from a range of technologies, to analyse and derive relationships between time, distance, displacement, speed, velocity and acceleration in rectilinear motion, including:**

**– `s=ut+1/2at^2`**

**– `v=u+at`**

**– `v^2=u^2+2as` (ACSPH061)**

### Calculations using Kinematic Equations

### What is Kinematics?

Kinematics is the branch of physics that deals with the motion of objects without considering the forces that cause the motion. It is one of the fundamental concepts in physics and is studied extensively in the NSW HSC Physics syllabus. In this article, we will discuss the kinematic equations, which are essential tools for analyzing the motion of objects.

### What are the Kinematic Equations?

The kinematic equations are a set of equations that relate the motion of an object to its initial velocity, final velocity, displacement, acceleration, and time. These equations are:

where:

s = displacement (in meters)

u = initial velocity (in meters per second)

v = final velocity (in meters per second)

a = acceleration (in meters per second squared)

t = time (in seconds)

These equations can be used to solve a variety of problems related to the motion of objects. Let's discuss each of them in detail.

### Equation 1: `v=u+at`

This equation relates the final velocity (v) of an object to its initial velocity (u), acceleration (a), and time (t). It states that the final velocity of an object is equal to its initial velocity plus the product of acceleration and time.

### Equation 2: `s=ut+1/2at^2`

This equation relates the displacement (s) of an object to its initial velocity (u), acceleration (a), and time (t). It states that the displacement of an object is equal to the product of its initial velocity and time plus half the product of acceleration and time squared.

### Equation 3: `v^2=u^2+2as`

This equation relates the final velocity (v) of an object to its initial velocity (u), displacement (s), and acceleration (a). It states that the final velocity of an object squared is equal to the initial velocity of an object squared plus twice the product of acceleration and displacement.

### Kinematic Equations Calculation Examples

Here are a few examples for you to practise using the kinematic equations. The working and solution of them can be found in the video above.

**Example 1**

A mass, initially at rest, accelerates in the north direction at 2.5 `m s^{-2}`.

Calculate the velocity and displacement after 2 s.

**Example 2**

A mass initially at rest undergoes a motion with uniform acceleration. After 10 s, the mass is 100 m from its original position.

(a) Calculate the acceleration of the mass.

(b) Calculate its instantaneous velocity at 10 s.

**Example 3**

A car accelerates at 8 `m s^{-2}` from 20 `m s^{-1}` to 36 `m s^{-1}`.

Calculate the displacement travelled by the car during this time.

**Example 4**

A car, initially travelling at 20 `m s^{-1}`, accelerates uniformly to 30 `m s^{-1}` in 5 s.

Calculate the displacement travelled by the car during this period.

**Example 5**

A mass, while moving at a constant velocity of 5 `m s^{-1}`, begins to accelerate at –2 `m s^{-2}`.

(a) After how many seconds will the mass come to a stop?

(b) What is the displacement of the mass at *t *= 10 s?

(c) What is the distance travelled in the first 10 s?

**Example 6**

During its launch from the Earth’s surface, a rocket accelerates uniformly to reach 12 000 `m s^{-1}` in 5 minutes, then maintains the constant speed for another 60 minutes.

What is the displacement of the rocket?