1.2 form 3 speed, velocity and acceleration
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This document defines key concepts related to motion including speed, velocity, acceleration, and deceleration. It provides definitions of scalar and vector quantities, and defines distance, displacement, speed, velocity, acceleration, deceleration, and average speed. Equations of motion are presented including relationships between velocity, acceleration, time and displacement. Examples are given to demonstrate calculations of speed, velocity, acceleration, distance and time from graphs and equations. Distance-time and velocity-time graphs are introduced and examples are worked through.
1.2 form 3 speed, velocity and acceleration
- 1. Speed, velocity and acceleration
- 2. 1. Scalar quantity 2. Vector quantity 3. Distance 4. Displacement 5. Speed 6. Velocity 7. Acceleration 8. Deceleration
- 3. Definitions 1. Scalar quantity: a quantity that has only magnitude. E.g. mass, temperature, distance e.t.c. 2. Vector quantity: a quantity that has both magnitude and direction e.g. weight, displacement, force, acceleration e.t.c. 3. Distance: this is the amount of space between two points. It is a scalar quantity and measured in meters, centimeters, kilometers, miles, light years e.t.c. The SI unit is meter (m). 4. Displacement: This is distance in a particular direction. E.g. 5km North, 15centimeters West
- 4. 5. (a) Speed: this is distance covered per unit time. It is a scalar quantity and is measured in meters per second (m/s), kilometers per hour (km/h), e.t.c. The SI unit for speed is meter per second (m/s). speed= distance (m) time (sec) (b) Average speed: this is given by: average speed = total distance (m) total time taken (s)
- 5. 6. Velocity: … is displacement per unit time. It is also defined as distance covered in a particular direction per unit time OR speed in a particular direction. It is a vector quantity and is measured in meters per second (m/s). For motion in a straight line, + or – is used to indicate direction: +10 m/s - 10 m/s
- 6. 7. Acceleration: this is change of velocity per unit time. It can also be defined as the rate change of velocity. It is a vector quantity. The SI unit is meters per second squared (m/s2) or (ms-2) 8. Deceleration: this is a negative acceleration. It is also called retardation.
- 7. Equations of motion 1. v = u + at 2. x = ut + 1/2 at2 3. V2 = u2 + 2ax 4. Vavg = V + u 2 5. Sp. = D/t Where; v = final velocity u = initial velocity vavg = average velocity a = acceleration t = time x = displacement Sp. = Speed D = Distance t = time
- 8. Examples 1. A car travels 600m in 30s. What is its average speed? 2. A car has a steady speed of 8m/s. a) How far does the car travel in 8s? b) How long does the car take to travel 160m? 3. A car takes 8s to increase its velocity from 10m/s to 30m/s. a) What is its acceleration? b) Calculate the distance covered. c) Determine its average velocity.
- 10. MOTION GRAPHS 1. Distance – time graphs - The distance covered by a car can be measured every second. This can be represented on a graph. - On a graph, the y- axis is the distance and the x-axis is the time taken. - The gradient is equal Time (s) Distance (m)
- 11. Exercise The distance traveled by truck was measured at intervals. The information was recorded in the table below. Use the information to draw a distance – time graph. Determine the speed of the truck a) between 1s and 3sec. b) between 4s and 6s Time/s 0 1 2 3 4 5 6 Distance/m 0 10 20 30 40 40 40
- 12. 2. Velocity – time graphs - For the speed time graph, velocity is on the y- axis and time on the x-axis. - The gradient of the graph is equal to the acceleration. Time (s) Velocity (m/s) The area under the graph is equal to the distance covered.
- 13. example
- 14. Exercise Consider the velocity – time graph below. 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 velocity(m/s) time (s) 1. Calculate the acceleration during the first 2 seconds. 2. What is the acceleration between the 2nd and 4th seconds of the motion? 3. Determine the deceleration. 4. Calculate; a. Distance covered in the first 2 seconds b. Total distance covered 5. Total distance covered