# Velocity-Time Graphs & Distance FINAL

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Category: Education

INFORMATIVE

## Presentation Transcript

### PowerPoint Presentation:

Velocity-Time Graphs & Distance

### Velocity-Time Graphs & Distance:

Velocity-Time Graphs & Distance To be able to calculate distance from a velocity-time graph

### Acceleration:

Acceleration Acceleration is the change in velocity (ΔV) ÷ time (t) Acceleration (a) Change In Velocity (ΔV) Time (t)

### Velocity-Time Graphs:

Velocity-Time Graphs Remember, the velocity of an object is its speed in a particular direction (this means that two cars travelling at the same speed, but in opposite directions, have different velocities) When an object is moving with a constant velocity, the line on the graph is horizontal When an object is moving with a constant acceleration, the line on the graph is straight, but sloped The steeper the line, the greater the acceleration of the object

### Acceleration:

Acceleration Acceleration is represented on a velocity-time graph by the gradient of the line (change in velocity ÷ time) What is the acceleration - represented by the sloping line? Change in velocity from 0m/s to 8m/s = 8m/s Time of 4 seconds for change in velocity 8 ÷ 4 = 2m/s 2

### Distance:

Distance The area under the line on a velocity-time graph represents the distance travelled What distance was covered on the above graph?

### Distance:

Distance To find the distance we need to calculate the area of the light blue and dark blue regions For rectangle areas use the formula base x height 6s x 8m/s = 48m For triangle areas use the formula ½ x base x height ½ x 4s x 8m/s = 16m Distance = 48 + 16 = 64m

### Graphing:

Graphing Let us revise and check our knowledge about graphs with the help of few questions.

### Question 1:

Question 1 Match A, B, C and D to the following descriptions: - Accelerated motion throughout Zero acceleration Accelerated motion, then decelerated motion Deceleration Which line represents the furthest distance? Which line represents the least distance?

Answer 1 Match A, B, C and D to the following descriptions: - Accelerated motion throughout – A ( 1/2 x 20s x 8m/s = 80m) Zero acceleration – C (20s x 8m/s = 160m) Accelerated motion, then decelerated motion – D ( 1/2 x 20s x 6m/s = 60m) Deceleration – B ( 1/2 x 20s x 4m/s = 40m) Which line represents the furthest distance? – C Which line represents the least distance? – B

### Question 2:

Question 2 Describe the motion of the cyclist Work out the initial acceleration Work out the distance travelled by the cyclist in the first 40 seconds

Answer 2 Describe the motion of the cyclist – accelerates at constant rate for 40 seconds, then decelerates for the next 20 seconds to a standstill Work out the initial acceleration – 0.2m/s 2 (8m/s ÷ 40s) Work out the distance travelled by the cyclist in the first 40 seconds – ½ x 40s x 8m/s = 160m

### Question 3:

Question 3 In a motorcycle test the speed from rest was recorded at intervals Time (s) 0 5 10 15 20 25 30 Velocity (m/s) 0 10 20 30 40 40 40 Plot a velocity-time graph of these results What was the initial acceleration? How far did it travel in the first 20 seconds? How far did it travel in the next 10 seconds?