# Activity: Acceleration and suvat Here you will define acceleration and come to understand its vector nature. You will learn how to calculate acceleration when it is constant and determine it using the gradient of a velocity vs. time graph. The 'suvat' equations of uniformly accelerated motion are derived and problems of constant acceleration are presented for you to solve.

#### Need to know

Doing this at home? This activity mainly uses simulations, however students will need to measure the acceleration due to gravity in real life. Measuring g (falling ball) uses a custom built system to measure the time that a ball takes to fall a known distance. The experiment can also be done using audacity to measure the time. This is an audio program; it will record the sound that a ball makes when it hits the ground so all you need to do is make a sharp sound when you let it go, tapping the computer with your finger nail works well. Highlight the gap between the peaks and the time interval is displayed at the bottom. Put your data into the table and follow the instructions as normal.

Acceleration

Acceleration is defined as the rate of change of velocity, so if velocity changes there must be acceleration. • If a car drives round a corner it must be accelerating even if the speed is constant, why?
• In this part of the course we are only interested in constant acceleration. This means the motion must be in a straight line, why?

SUVAT

SUVAT doesn't mean anything, the letters just represent the different quantities in the motion that we will consider.

• s is displacement
• u is initial velocity
• v is final velocity
• a is acceleration
• t is time interval • According to the diagram does the velocity get bigger or smaller? How can you tell?
• Is the acceleration positive or negative?

For this motion Calculate the acceleration for:

• A body travelling at $$4\text{ m s}^{-1}$$ accelerates to $$8\text{ m s}^{-1}$$ in $$2\text{ s}$$.
• A body travelling at $$8\text{ m s}^{-1}$$ slows down to $$2\text{ m s}^{-1 }$$ in $$2\text{ s}$$.

The sign of acceleration

Acceleration is a vector so its sign gives its sense or (in 1 dimension) its direction: + forwards - backwards.

• When a body is dropped its acceleration is -9.8 ms-2 . What is the significance of the - sign?

The diagram below shows a ball travelling to the left • Taking right to be + and left - calculate the acceleration.

Note that the acceleration is - even though the ball is getting faster. Remember that sign gives direction.

Measuring acceleration

To measure acceleration, you need two velocities and a time.

Here is an accelerating $$1\text{ cm}$$ long rectangle. You can run the simulation by clicking the play button or advance it slowly with the slider

• Determine the initial velocity ($$u$$) by measuring the time it takes to pass through the first marker.
• Determine the final velocity ($$v$$) as it passes through the second marker.

Since the card is small we can take these velocities to be instantaneous velocities. The rectangle would be travelling at these velocities when the rectangle is in the middle of the marker.

• Measure the time taken from one marker to the other.
• Calculate the acceleration of the rectangle. You should get $$0.015\text{ m s}^{-2}$$.

Graphing the motion

Another accelerating object for you, but this time a red ball and the velocity is displayed so you don't need to measure all the times. The horizontal scale is in meters.

• In LoggerPro make a table of displacement and time.
• Plot a graph of displacement vs time.
• What shape does the graph have?
• Try fitting a curve to the points.
• Open a new LoggerPro file.
• Record the velocity and time at each meter.
• Plot a graph of velocity against time.
• Find the acceleration from the slope of the line (should be $$0.5\text{ m s}^{-2}$$).

The 'suvat' equations So far we have two equations that define this motion

From the definition of acceleration: (1)

and average velocity: (2)

It might seem strange that the average is found by adding the max + min and dividing by 2 but this works because the acceleration is constant like the heights of the following students. Manipulating the equations

Any problem can be solved using these two equations for example:

Find the distance travelled by a body with initial velocity 5 ms-1 accelerating with acceleration 2 ms-2 for 10 s.

• rearrange equation (1) to make v the subject
• find v
• use this value of v to find s from equation (2)

This could be done in one step if we combined the equations.

• rearrange (1) to make v the subject
• substitute for v in (2)
• simplify to give Here's another one:

• rearrange (1) to make t the subject
• substitute for t in (2)
• simplify and make v2 the subject to give Use these equations to solve the exercise on page 43.

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