Calculating Acceleration

The meaning of acceleration     

In everyday language, the term accelerating means “ speeeding up “. Anything whose speed is increasing is accelerating. Anything whose speed is decreasing is decelarating. To be more precisi in our definition of acceleration, we should think of it as changing of which is changing its direction has acceleration. Because acceleration is linked to velocity in this way, it follows that is a vector quantity. Example of objects acceerating is A car speeding up as it leaves the town, the driver presses on the accelerator pedal to increase the car’ velocity.

Calculating acceleration

          The acceleration of something indicates the rate at which its velocity is changing.  Languange can get awkward here. We might say “ the sprinter accelerates faster than the car”. However, “faster” really means “greater speed”. So it is better to say  “ the sprinter has a greater acceleration than the car. Acceleration is defined as follows :

                   Acceleration = rate of change of velocity

                   Acceleration =  Change in velocity / time taken

                                                

So to calculate accelaration a, we need to know two quantities, the change of velocity  delta v and time taken delta t.

                   a = v / t

Sometimes this equation is writte differently. We write u for the initial velocity and v for the final vlocity ( because u comes before v in the alpabet). The moving object accelarates from u to v in a time t ( this is the same as the time rpresented bg delta t above). The accelerationis given by the equation :

                   a = v – u / t

                           

Example

1.     Leaving a bus stop, the bus reaches a velocity of 8.0 m/s after 10 s. Calculate the accelaration of the bus.

Step 1 : Note the bus initial velocity is 0 m/s. Therefore :
             change in velocity ( delta v ) = ( 8.0 - 0)m/s

             Time taken ( delta t ) = 10 s

Step 2 : Subtitute these values in the equation for acceleration :

              acceleration a = delta v/ delta t = 8.0 / 10 = 0.8 m/s square     

2.    A sprinter starting from rest has an acceleration of 5.0 m/s square during the first 2.0 s of race. Calculate her velocity after 2.0 s.

Step 1 : Rearranging the equation a = v - u / t , gives : v = u + at

Step 2 : Subtituting the values and calculating gives :

              V = 0 + ( 5.0 x 2.0 ) = 10 m/s

Hope it usefull :)