Calculating Total Acceleration on an Outdoor Track

[teng125]

an outdoor track is 65m.A runner increases her speed at a constant rate from 4 to 7 m/s over a distance of 30m.Determine the total acceleration of the runner 2s after she begins to increase her speed.


the answer is 0.680m/s^2

 

[Integral]

Could you show us some of your thoughts. What is the relationship between velocity and acceleration?

 

[teng125]

the relation is dv/dt=a.But how can i form eqn??

 

[Hootenanny]

You have the linear speeds and the distance traveled while accelerating, use the equations of motion to calculate the linear acceleration - remember this is a consant acceleration.

 

[teng125]

may i know what's the eqn of motion that u mean??

 

[cscott]

may i know what's the eqn of motion that u mean??

$$a = \frac{v^2 - v_0^2}{2d}$$

 

[teng125]

is it possible to use acce normal + acce tangential formula??

 

[Fermat]

The formula given by cscott is for the tangential acceleration of the girl going round the track. That is a constant value.
Now you have to find the radial accelerartion, which is not constant. Do you know why ?
Ans: Because a_r = v²/r and v is constantly changing (in white)
You have to find the peripheral velocity, or speed, at t = 2 sec. From that find the radial accln. Then use pythagoras' theorem with the tangential and radial accln to get the total accln.