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Average Speed The speed of an object is the distance it travels a certain time. 10 ms-1 means 10 m travelled in one second. 50 kmh-1 means 50 km travelled in one hour. Speeds usually vary throughout a journey. For this reason, we often calculate the average speed of an object. Measuring Average Speed stopwatch t d Mark out and measure a distance d. Measure the time taken, to travel distance d. Calculate the average speed using: distance average speed time d ÷ v t Quantity Unit speed ( v ) metre per second ( ms-1 ) distance ( d ) metres ( m ) time ( t ) seconds ( s ) x Example 1 A van has an average speed of 10 ms-1. Calculate the time it takes the van to travel a distance of 125 m. v 10 ms -1 d 125 m t ??? t d v 125 10 t 12.5 s Results (running) d= m t= s v = ??? d v t v ms -1 Results (walking) d= m t= s v = ??? d v t v ms -1 Instantaneous Speed Instantaneous speed is the speed at a particular instant. This means it is a very short distance travelled. Length of Card Light Gate Electronic Timer The card on the trolley cuts the light beam. The timer starts when the beam is broken. The timer stops when the light beam is restored. The instantaneous speed is calculated by: instantane ous speed length of card time taken Q1. Why is an electronic timer used rather than a stopwatch? Human reaction time would give an inaccurate time. Q2. How could a more accurate instantaneous speed be recorded? Shorter length of card. Example 1 A trolley with a card attached to it travels down a ramp and passes through a light gate. The light beam is interrupted for 0.24 s. Calculate the instantaneous speed of the trolley as it passes through the light gate. card width 6 cm 0.06 m interrupte d time 0.24 s instantane ous speed ??? length of card instantane ous speed time taken 0.06 0.24 instantane ous speed 0.25 ms -1 Acceleration The acceleration of an object is its change in speed in one second. v - u ÷ a t x Quantity Unit Acceleration ( a ) Metre per second per second ( ms-2 ) Final Speed ( v ) Metre per second (ms-1 ) Initial Speed ( u ) Metre per second (ms-1 ) Time (t) Seconds (s) Example 1 A car accelerates from a speed of 5 ms-1 to a speed of 15 ms-1 in a time of 2.5 seconds. What is its acceleration? a u 5 ms -1 v -u t v 15 ms -1 t 2.5 s a ??? 15 - 5 2.5 10 2.5 a 4 ms 2 An acceleration of 4ms-2 means that the speed increases by 4ms-1 every second. Answer the following questions showing ALL your working Car Initial Speed (ms-1) Final Speed (ms-1) Time (s) Acceleration (ms-2) Lamborghini 0 28 3.3 8.5 Chevrolet 0 28 3.7 7.6 Aston Martin 0 28 4.8 5.8 Mondeo 0 28 9.9 2.83 Deceleration Deceleration is when an object slows down. The formula a v u is still used but u (initial speed) will be t greater than v (final speed). Example 1 A car decelerates from 12 ms-1 to 2 ms-1 in 5 seconds. Calculate the deceleration. a u 12 ms -1 v -u t v 2 ms -1 t 5s a ??? 2 - 12 5 - 10 5 a -2 ms 2 Example 2 A car travelling at 15 ms-1 comes to rest in a time of 4 seconds. Calculate the car’s deceleration. a u 15 ms -1 v -u t v 0 ms -1 t4s a ??? 0 - 15 4 - 15 4 a -3.75 ms 2 Deceleration is always negative. Acceleration at Credit Level Will need to rearrange equation to calculate initial speed (u) and final speed (v). Final Speed (v) v -u a t v - u ÷ a t x a t v u v -u a t v u at *** NEW FORMULA *** Not on data sheet – memorise. Example 1 A car accelerates at 2.5 ms-2 for 3 seconds. The initial speed of the car is 4 ms-1. Calculate the final speed of the car. a 2.5 ms -2 v u at t 3s 4 2.5 3 u 4 ms -1 v ??? 4 7.5 v 11.5 ms 1 Initial Speed (u) Use the equation rearrange. v u at and substitute the numbers and Example 2 A car reaches a speed of 20 ms-1 after accelerating at 2 ms-2 for 4 seconds. Calculate the initial speed of the car. v u at v 20 ms -1 a 2 ms -2 t4s u ??? 20 u 2 4 20 u 8 u 8 20 u 20 - 8 u 12 ms -1 Speed-Time Graphs v v t acceleration v t constant speed t deceleration Steeper lines mean quicker acceleration / deceleration. speed (ms-1) 12 2 1 0 3 10 3 14 time (s) The motion of the object is in 3-sections. Section 1 Object accelerates from rest. Section 2 Object travels at a constant speed of 12ms-1. Section 3 Object decelerates and comes to a halt. Example 1 speed (ms-1) 20 0 11 4 time (s) (a) Describe the 3-parts of the journey. (b) Calculate the initial acceleration. (c) Calculate the final deceleration. 14 (a) (b) Describe the 3-parts of the journey. Part 1 Object accelerates from rest to 20ms-1. Part 2 Object travels at a constant speed. Part 3 Object decelerates from 20ms-1 to rest. Calculate the initial acceleration. a u 0 ms -1 v 20 ms t4s a ??? -1 v -u t 20 - 0 4 20 4 a 5 ms 2 (c) Calculate the final deceleration. v -u a t v 0 ms -1 u 20 ms t 3s a ??? -1 0 - 20 3 - 20 3 a 6.67 ms 2 Example 2 16 3 10 speed (ms-1) 4 2 1 0 4 2 5 56 11 14 time (s) (a) Describe motion of the object for each section of the graph. (b) Calculate the acceleration for section 1 and 3 of the graph. (c) Calculate the final deceleration of the object. (d) What is the acceleration at section 4 of the graph? Total Distance Travelled The total distance travelled can be calculated from a speed-time graph. Total Distance Travelled = Area Under Speed-Time Graph Example 1 speed (ms-1) 12 2 1 0 3 10 3 time (s) Calculate the total distance travelled. 14 Total Distance = Area Under Graph = Area 1 + Area 2 + Area 3 Area 1 Area 2 1 bh 2 1 3 12 2 area 18 m Area 3 7 12 84 m The total distance travelled is: 1 bh 2 1 4 12 2 area area l b 18 84 24 24 m 126 m The average speed over the whole journey can now be calculated. average speed total distance total time 126 14 9 ms -1 Example 2 A driver approaches traffic lights in his car. He sees the lights change and brakes. The speed time graph of the car, from the instant that the lights change is: speed (ms-1) (a) Describe the motion of the car in the first 0.5 s. (b) Calculate the deceleration of the car. (c) Calculate the distance travelled by the car after the brakes were applied. 6 0 3 0.5 time (s) (a) Explain the shape of the graph in the first 0.5 s. During the first 0.5 s of the journey, the car is travelling at a constant speed of 6 ms-1. (b) Calculate the deceleration of the car. a u 6 ms -1 t 2.5 s v 0 ms -1 a ??? v -u t 0-6 2.5 -6 2.5 a 2.4 ms 2 (c) Calculate the distance travelled by the car after the brakes were applied. Distance Travelled = Area Under Speed-Time Graph distance travelled area of triangle 1 bh 2 1 2.5 6 2 7.5 m