P2aL2 Speed isn't Everything

Key Words

Acceleration - change in speed divided by time.

Constant velocity - speed in a direction that has the same direction and the same value.

Direction - towards a particular point

Distance - length between two points

Distance time graph - a graph in which distance (vertical axis) is plotted against time (horizontal axis).

Gradient - the steepness of the slope.  Gradient = rise ÷ run.

Negative velocity - speed in the opposite direction to positive velocity

Positive velocity - speed in a particular direction.

Speed - distance divided by the time.

Velocity - speed in a particular direction.

Velocity time graph - a graph in which velocity (vertical axis) is plotted against time (horizontal axis).

Test Yourself

Homework
Physics GCSE
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Grade E

Velocity is NOT a posh word for speed.  It is speed in a particular direction.  If we say that left to right is positive, an object travelling at 2 m/s from left to right has a positive velocity of +2 m/s.  In exams, they may give you the direction that is positive.  If not, choose which way you want to be positive, and stick to it.

If the object is travelling at 2 m/s from right to left, it has a negative velocity of -2m/s.

Velocity has the physics code v.  It is worked out using the equation:

velocity (m/s) = displacement (m) ÷ time (s)

Displacement is distance in a particular direction; the physics code is s.  Time is t.

Upwards moving objects have a positive velocity.  Downwards moving objects have a negative velocity.

An aeroplane flying at 60 m/s in level flight has a horizontal velocity of 60 m/s forward, but a velocity of 0 m/s away from the ground.  This is because it is going neither up nor down.

 

We can represent velocity using a velocity time graph:

In this case the velocity is constant at 3 m/s.

If the velocity changes at a constant rate, the velocity time graph is a straight line.  The slope gives the acceleration:

If the slope is negative, the acceleration is negative.  The vehicle is slowing down.

A tachograph on a lorry or a train is a speed time graph.

Grade C

Acceleration is defined as:

Acceleration (m/s2) = change in velocity (m/s)

                                     time (s)

The change in velocity = velocity at end - velocity at the start

Acceleration is a vector, which means it has a value and a direction.

If an object is travelling from left to right (positive velocity) and the acceleration is also from left to right, the velocity increases.  If the acceleration is from right to left, then it is negative.  It will be in the opposite direction and the object's velocity will reduce.  If the time interval is long enough the object will go backwards.

Negative acceleration can also be described as deceleration.

The acceleration due to gravity is always downwards, and considered to be negative acceleration.

Acceleration is always in the direction of an unbalanced force.

 

The gradient of the velocity time graph gives the acceleration.  The steeper the slope, the more the acceleration.  The velocity time graph below shows a train accelerating from a station, maintaining a constant speed of 50 m/s, then slowing down a "double yellow" caution signal to 20 m/s.  It then passes a "single yellow" caution signal, and finally stops at a red signal.

The area under the graph gives the distance travelled.

The area under the graph can be found by working out the areas of:

  • Triangles A, C, and F;

  • Rectangles B, D, and E.

You would add these all together to get the total distance the train travelled in the 400 s.

 

Grade A

In the higher paper, you would need to be able to work out the gradient of the velocity time graph to get the acceleration.  You also need to work out the area under the graph to get the total distance travelled.

Let us work out the acceleration:

Gradient = rise/run = 50 m/s ÷ 100 s = 0.5 m/s2

Now we can work out the deceleration at triangle C:

Deceleration = (20 - 50) m/s ÷ 50 s = -30 m/s ÷ 50 s = -0.6 m/s2

Note the negative sign to indicate that there is negative acceleration.

 

To work out the area under the graph, we need to know that for a triangle, Area = 1/2 base × height

  • For A, area = 1/2 × 100 s × 50 m/s = 2500 m.

  • For C, area = 1/2 × 50 s × 30 m/s = 750 m.

  • For F, area = 1/2 × 50 s × 20 m/s = 500 m

For the rectangles:

  • For B, area = 150 s × 50 m/s = 7500 m.

  • For D, area = 50 s × 20 m/s = 1000 m.

  • For E, area = 50 s × 20 m/s = 1000 m

So we add up all the areas:

2500 m + 7500 m + 750 m + 1000 m + 1000 m + 500 m = 13250 m

The average speed = total distance ÷ total time = 13250 m ÷ 400 s = 33.1 m/s

If the graph is not obligingly made of rectangles and triangles, you can count the squares under the graph.  At GCSE, they are.

 

 

In circular motion, the speed of an object going round in a circle is constant.  However the direction of the object is always changing, so the velocity is changing.  The direction is always towards the centre of the circle.  Changing velocity is the result of acceleration.

Since acceleration is always the result of a force, there is a force acting towards the centre of the circle called the centripetal ("centre-seeking") force .

  There is no such thing as centrifugal force.