Remind pupils that this is a speed-time graph and ask, "How do we find the distance travelled on a speed-time graph?". Then, ask pupils to calculate how far each particle has travelled at the point of intersection.

Keywords

Gradient - The gradient is a measure of how steep a line is. It is calculated by finding the rate of change in the $$y$$-direction with respect to the positive $$x$$-direction.
Tangent - A tangent of a circle is a line that intersects the circle exactly once.

A powerful starter is to give students a distance-time graph and ask, "How much information can we obtain from this graph? What does it tell us?". Then, do the same activity for a speed-time graph.

Teacher tip

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Starter quiz

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6 Questions

Q1.

This speed-time graph shows __________ rate of change between time and speed.

Correct answer: a constant

an increasing

a decreasing

a fast

Q2.

What speed is this vehicle travelling at after $$10$$ seconds? m/s

Correct Answer: 50

Q3.

What distance has this vehicle travelled after $$10$$ seconds? m/s

Correct Answer: 250

Q4.

Which equation generalises how far this vehicle has travelled after $$x$$ seconds?

$$A={{x^2}\over{2}}$$

$$A=5x$$

$$A=5x^2$$

$$A={{5x}\over{2}}$$

Correct answer: $$A={{5x^2}\over{2}}$$

Q5.

What is the $$y$$-coordinate at the point of intersection of the two linear equations $$y=2x-10$$ and $$y=-{1\over2}x+5$$ ?

Correct Answer: 2, y=2

Q6.

What is the equation of the tangent to the circle at point A?

$$y=-{2\over5}x+{34\over5}$$

$$y=-{5\over2}x+1$$

Correct answer: $$y={5\over2}x+1$$

$$y={5\over2}x+11$$

$$y={5\over2}x-{27\over2}$$

Exit quiz

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6 Questions

Q1.

The __________ to a circle from an external point are equal in length.

radii

Correct answer: tangents

perpendiculars

Q2.

What is the tangent to the circle at A?

$$y=4x-14$$

$$y={1\over4}x+{29\over4}$$

Correct answer: $$y=-{1\over4}x+{29\over4}$$

$$y=-{1\over4}x-{29\over4}$$

$$y=-{1\over4}x+{13\over2}$$

Q3.

Find the point of intersection of the tangents to the circle from points A and B.

Correct answer: $$(21,2)$$

$$(2,21)$$

$$(19,2)$$

$$(23,2)$$

Q4.

Tangents from A and B meet at point C. To show that AC $$=$$ BC we would use __________.

a ruler

Correct answer: Pythagoras theorem

circle theorem

$$A=\pi \times r^2$$

Q5.

How far have these cars travelled between $$0$$ and $$6$$ seconds?

Both have travelled $$30$$ metres each

Both have travelled $$90$$ metres each

'a' has travelled $$90$$ metres and 'b' has travelled $$120$$ metres

Correct answer: 'a' has travelled $$90$$ metres and 'b' has travelled $$135$$ metres

'a' has travelled $$250$$ metres and 'b' has travelled $$275$$ metres

Q6.

After how many seconds will car 'a' overtake car 'b'? seconds.

Correct Answer: 12