## MATH - SCIENCE INTEGRATION

### Calculating Acceleration

 In mathematics you don't understand things. You just get used to them. Johann von Neumann (1903 - 1957)

### Methods for Solving Problems

 Solving acceleration problems require some of the same measurements needed for speed and velocity.                                                       The procedure for solving an equation concerning acceleration still requires the careful step-by-step process used in speed and velocity problems. Let's begin.

• Procedure for Solving Acceleration Problems
 EQUATION FOR ACCELERATION:   acceleration = final velocity – initial velocity =   D v                                                time                            t OR a =  vf – vi   =   D v            t              t As always, the best way to learn is to do!  Let's work through a problem. If you need to review solving one step division or subtraction problems, click below.

• Acceleration of a Skater
 Problem #1:   A skater goes from a standstill to a speed of 6.7 m/s in 12 seconds.  What is the acceleration of the skater?

 Step 1:   Write down the equation needed for solving for acceleration. a =  vf – vi   =   D v            t              t

 Step 2:   Insert the known measurements into the equation. Known :  The initial speed of the skater was zero since he was not in motion.  The skater finally reached a speed of 6.7m/s in 12 seconds, which is the final speed or velocity.  The equation will look like this: a = 6.7m/s – 0m/s = 6.7m/s =                12s              12s

 Step 3:   Solve.  Carefully put all measurements into your calculator. You must solve the change in velocity portion of the equation before you can do the division portion to solve for acceleration.  Don't forget that the SI unit for acceleration is m/s2  . SOLUTION:  The skater had an acceleration of  .56m/s2 . a = 6.7m/s – 0m/s = 6.7m/s = .56m/s2               12s              12s

 Now, you give it a try!

• Acceleration Practice Problems
 PRACTICE PROBLEMS: 1.   As a shuttle bus comes to a normal stop, it slows from 9.00m/s to 0.00m/s in 5.00s.  Find the average acceleration of the bus.       2.    During a race, a sprinter increases from 5.0 m/s to 7.5 m/s over a period of 1.25s.  What is the sprinter’s average acceleration during this period? 3.   A baby sitter pushing a stroller starts from rest and accelerates at a rate of  0.500m/s2.  What is the velocity of the stroller after it has traveled for 4.75 minutes?

 Ready to try some acceleration problems that are a bit more challanging?  Make sure that you have your paper, pencil, and calculator ready and then click here. Just can't get enough of those acceleration problems?  Then keep going!   Click here .

### Isolating a variable

 Not all problems dealing with acceleration are looking for the acceleration of an object.   Maybe the acceleration of the object is already known and the problem is to find the initial velocity of the object or the time interval that the object was accelerating.  In these cases, you will need to isolate the part of the problem for which you are looking.  This is known as isolating a variable. If you look below, you will see the acceleration equation as you have been practicing it.  You will also see the equation rearranged to find the velocity and the time.

 To find the acceleration  of an object: a= vf - vi  = D v        t               t

 To find the change in velocity  of an object: D v = (a)(t)

 To find the time  it took for an object to accelerate: t = D v        a

 These formulas are used by placing the know values given in the problem into the equation.  Always ask yourself, "What is the problem solving for?" or "What is the problem looking for?",  and then choose the correct formula. Let's practice a few of these types of problems.

• Practice Problems: Solving for Speed
 Solving for speed:

 A bicyclist accelerates at 0.89m\s2 during a 5.0s interval.  What is the change in the speed of the bicyclist and the bicycle? A freight train traveling with a speed of 18.0m/s begins braking as it approaches a train yard.  The train’s acceleration while braking is -0.33m/s2.  What is the train’s speed after 23 seconds? A skater travels at a constant velocity of 4.5m/s westward, then speeds up with a steady acceleration of 2.3m/s2.  Calculate the skater’s speed after accelerating for 5.0s.

• Practice Problems: Solving for Time
 Solving for Time:

 Marisa’s car accelerates at an average rate of 2.6m/s2.  Calculate how long it takes her car to accelerate from 24.6m/s to 26.8m/s. If a rocket undergoes a constant total acceleration of 6.25m/s2, so that its speed increases from rest to about 750m/s, how long will it take for the rocket to reach 750m/s.   A dog runs with an initial speed of 1.5m/s on a waxed floor.  It slides to a stop with an acceleration of -0.35m/s2.  How long does it take for the dog to come to a stop?