1.2.1 Acceleration. Some interesting statistics about top fuel dragsters::

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1 1.2.1 Acceleration Some interesting statistics about top fuel dragsters:: One Top Fuel dragster 8.2 L. Hemi engine makes more horsepower than the first 4 rows at the Daytona 500. A stock Dodge Hemi V8 isn t powerful enough to drive the supercharger on a dragster. Dual magnetos supply 44 amps to each spark plug (the output of an arc welder). If spark momentarily fails early in the run, unburned nitro builds up in the affected cylinders and then explodes with sufficient force to blow cylinder heads off the block in pieces or split the block in half. In order to exceed 480 km./hr. in 4.5 seconds dragsters must accelerate at an average of over 4G's. In order to reach 320 km./hr. well before half-track, the launch acceleration approaches 8G's. Dragsters reach over 480 km./hr. before you have completed reading this sentence. The Bottom Line; Assuming all the equipment is paid off, the crew worked for free, and for once NOTHING BLOWS UP, each run costs an estimated US $1, per second. Putting all of this into perspective: Imagine that you re driving the $140,000 Lingenfelter "twin-turbo" powered Corvette Z06. Over a mile up the road, a Top Fuel dragster is staged and ready to launch down a quarter mile strip as you pass. You have the advantage of a flying start. You run the 'Vette hard up through the gears and blast across the starting line and past the dragster at an honest 300 km./hr. The 'tree' goes green for both of you at that moment. The dragster launches and starts after you. You keep your foot down hard, but you hear an incredibly brutal whine that sears your eardrums and within 3 seconds the dragster catches and passes you. He beats you to the finish line, a quarter mile away from where you just passed him. Think about it, from a standing start, the dragster had spotted you 300 km./hr. and not only caught, but nearly blasted you off the road when he passed you within a mere 400 m. race course. That s ACCELERATION. Page 1 of 12

2 Acceleration is defined as: the rate of change of velocity. There are two types of acceleration: 1.2.1a Average Acceleration Defined as: the total change in velocity divided by the total change in time Calculated using: (1.3) 1.2.1b Instantaneous Acceleration Defined as: the acceleration at some instant in time Calculated using: the instantaneous slope of a velocity time graph. Eg.#1 What is the difference between velocity and acceleration? Acceleration deals with change of velocity; velocity deals with change of position Eg. #2 A track runner starting from rest, reaches a velocity of 9.3m/s [fwd] in 3.9 s. Determine the runner s average acceleration. Eg.#3 The Renault Espace F-1 is a modified production car that can go from rest to 100. km/hr 2 with an average acceleration of 9.52m/s [fwd]. How long does it take the Espace F-1 to achieve its final speed of 100. km/hr? Page 2 of 12

3 Eg.#4 After hitting the target, an arrow undergoes 3 2 an average acceleration of m/s [W] in s, then stops. Determine the initial velocity of the arrow when it hit the target Graphing Accelerated Motion Eg.#5 A graph of position vs. time of a dynamics cart is shown below: Page 3 of 12

4 a) Draw a smooth curve through the data points, use it to calculate the slopes of the curve at each data point and record in the table below: Velocity Time Data Time (s) Velocity (m/s[n]) b) What does the slope represent? c) Graph the data in the table above onto the graph paper below and join the data points with a straight line. Page 4 of 12

5 d) Calculate the slope of the straight line. e) What does this slope represent? The slope represents the acceleration. Eg.#6 The acceleration vs time graph of the motion of a car initially at rest is shown: a) Find the area of the 3 rectangles in the graph above and record in the table: b) What do the areas represent? The change in velocity of the car during each interval. Time (s.) Area (m./s.[n.]) m/s m./s.+24m./s. = 42m./s m./s.+10.5m/s = 52.5m./s. Page 5 of 12

6 c) Draw the associated velocity time graph below (remember, the car was initially at rest): d) Calculate the total area under the graph at each of the times in the table below: Time (s.) Position (m.[n.]) m m.+99m. =135m m.+141m. =276m. e) What are the dimensions of the area? metres [N.] f) What do these quantities represent? The change in position (displacement) Page 6 of 12

7 1.2.3 Graphing Accelerated Motion Summary Eg.#7 What do each of the following represent? Type of graph Area Under Slope of a Tangent Line Slope of a Secant Line position vs time no meaning instantaneous velocity average velocity velocity vs time change of position (displacement) instantaneous acceleration average acceleration acceleration vs time change of velocity instantaneous rate of change of acceleration average rate of change of acceleration Eg.#8 Describe the motion depicted in each graph below: a) b) object slows down uniformly then briefly stops object slows down uniformly until it object accelerates uniformly stops c) d) constant positive acceleration from rest followed by larger positive acceleration instantaneous changes in acceleration followed by negative acceleration Page 7 of 12

8 1.2.4 Solving Constant Acceleration Problems So far, we ve used the equation to solve problems. Sometimes however we are not given all of these quantities. We need other kinematics equations. Formula Variables Involved Variables Missing (1.2) (1.3) (1.4) (1.5) 2 Eg.#9 A ball rolls down a hill, starting from rest, with an acceleration of 1.0 m/s [down the hill]. a) What is the velocity of the b) How far did the ball travel after 9.0 ball after 7.0 seconds? seconds? Page 8 of 12

9 1.2.5 Acceleration in Two Dimensions We saw earlier that. This equation also applies in 2 dimensional situations. The catch is that is a vector subtraction. Eg.#10 Calculate the acceleration of a car that travels initially at 80. km/hr [N] and after accelerating for 2.5 seconds is now traveling at 100. km/hr [N30 E] Page 9 of 12

10 Worksheet What condition must be true so that instantaneous acceleration and average acceleration are equal? If the acceleration is uniform, the average and instantaneous acceleration will be equal 2. An aircraft while preparing to land changes its velocity from 1650km./hr.[W] to 1120 km./hr.[w] in a time of 345 seconds. Calculate the average acceleration of the aircraft in a) (km./hr.)/s. b) m./s Sketch a graph of a car that has increasing speed and decreasing acceleration during a time of 4.0 seconds. 4. Describe the motion depicted by each graph shown below: a) The motion starts at a specific location with a high velocity and a negative acceleration, reaching zero velocity midway through the motion. The motion then undergoes increasing velocity in the opposite direction until reaching the initial position. Page 10 of 12

11 b) The velocity increases at a uniform rate in the positive direction, followed by a decreasing velocity in the same direction until nearly stopping at the end of the motion. c) The motion starts with uniform velocity, then accelerates at a high rate for a short time before slowing down with a negative acceleration at a lower rate until the velocity reaches zero at the end of the motion. 5. A car, initially travelling at 26m./s.[E] slows down with a constant average 2 acceleration of 5.5m./s. [W]. Determine its velocity after 2.5 seconds. 6. A bullet, starting from rest exits the 0.56m. long barrel of a gun, after accelerating along its length with a velocity of 420. m./s.[fwd]. a) What is the average velocity of the bullet in the barrel? Page 11 of 12

12 b) What is the average acceleration of c) How long does it take the bullet to the bullet in the barrel? travel the length of the barrel? 7. A car (C) and a van (V) are stopped beside one another at a red light. When the light turns green, the motion of each vehicle is as shown in the graph below: a) After the light turns green, when do both vehicles have the same velocity? Both vehicles have the same velocity at b) After the light turns green, when does the van overtake the car? Page 12 of 12