There are a number of equations of motion:

Where:

• $s$ is displacement
• $u$ is initial velocity
• $v$ is final velocity
• $a$ is acceleration
• $t$ is time

Example 1:

A particle is moving with an initial velocity equal to 2 ms⁻¹ in a positive direction. Its final velocity after traveling a distance of 20 m is 23 ms⁻¹. Assuming constant acceleration, find the acceleration of the particle.

Given:

• S = 20 m
• U = 2 ms⁻¹
• V = 23 ms⁻¹
• a = ? Using the equation:

Substituting the values:

Simplifying:

Example 2:

A particle is traveling with an initial velocity of 16 ms⁻¹ and over a distance of 350 m, accelerates at a rate of 8 ms⁻². Find the time taken to travel the 350 m journey.

Given:

• S = 350 m
• U = 16 ms⁻¹
• a = 8 ms⁻²
• t = ? Using the equation:

Substituting the values:

Simplifying:

Using the quadratic formula, the time $t$ is approximately 7.57 s.

Example: 3

A particle accelerates uniformly. Initially, it has a speed of 6 ms⁻¹, then after 12 seconds, it has a speed of 6 ms⁻¹ in the opposite direction. Find the acceleration of the particle.

Given:

• $U = :highlight[6 ms⁻¹]$
• $V = :highlight[-6 ms⁻¹]$
• $a = ?$
• $t = :highlight[12 s]$ Using the equation:

Substituting the values:

Simplifying:

Note: A negative acceleration is called deceleration.