Constant Acceleration

Constant acceleration graphs

It is possible to graphically represent the motion of an object. In this section, we will look at two types of graphs that are commonly used for representing the motion of an object moving with constant acceleration:

1. Displacement-time graphs

2. Velocity-time graphs

Displacement-time graphs

The motion of an object can be represented using a displacement-time graph.

Displacement is represented on the Y-axis and time (t) on the X-axis. This implies that the change of position of the object is plotted against the time it takes to reach that position.

Here are a few things to keep in mind for displacement-time graphs:

• Since velocity is the rate of change of displacement, the gradient at any point gives the instantaneous velocity at that point.

• Average velocity = (total displacement)/(time taken)

• If the displacement-time graph is a straight line, then the velocity is constant and the acceleration is 0.

Velocity-time graphs

The motion of an object can also be represented using a velocity-time graph. Customarily, the velocity (v) is represented on the Y-axis and time (t) on the X-axis.

Here are a few things to keep in mind for velocity-time graphs:

• Since acceleration is the rate of change of velocity, in a velocity-time graph the gradient at a point gives the acceleration of the object at that point.

• If the velocity-time graph is a straight line, then the acceleration is constant.

• The area enclosed by the velocity-time graph and the time-axis (horizontal axis) represents the distance travelled by the object.

• If the motion is in a straight line with positive velocity, then the area enclosed by the velocity-time graph and the time-axis also represents the displacement of the object.

Constant acceleration equations

For a body moving in a single direction with constant acceleration, there is a set of five commonly used equations that are used to solve for five different variables. The variables are:

1. s = displacement
2. u = initial velocity
3. v = final velocity
4. a = acceleration
5. t = time taken

The equations are known as the constant acceleration equations or the SUVAT equations.

The SUVAT Equations

There are five different SUVAT equations that are used to connect and solve for the variables above in a system of constant acceleration in a straight line.

1. \(v = u + at\)
2. \(s = \frac{1}{2} (u + v) t\)
3. \(s = ut + \frac{1}{2}at^2\)
4. \(s = vt - \frac{1}{2}at^2\)
5. \(v^2 = u^2 + 2 as\)

Constant acceleration due to gravity

The force of gravity exerted by the Earth causes all objects to accelerate towards it. As we have already discussed, an object falling from a height falls with practically constant acceleration. If we ignore the effects of air resistance and the almost negligible gravitational pull of other objects, this would be perfectly constant acceleration. The acceleration due to gravity also does not depend on the mass of the object.

The constant g is used to represent the acceleration due to gravity. It is approximately equal to 9.8 m / s². If you are solving problems that require you to use the value of acceleration due to gravity, you should use the value g = 9.8 m / s² unless a more accurate measurement is provided to you.

A body falling from a height can be considered a body accelerating at a rate of g. A body being thrown up with an initial velocity can be considered a body decelerating at a rate of g until it reaches its peak height where the acceleration is zero. When the object falls after reaching its peak height, it will accelerate again at a rate of g while going down.