Question:A cyclist is riding with a speed of $7.5$ m/s. As he approaches a circular turn on the road of radius $80m$, he applies brakes and reduces his speed at the constant rate of $0.50$ m/s every second. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn ?

My approach:I know that if I can find the centripetal acceleration($a_c$) and tangential acceleration($a_t$) then I can easily calculate their resultant and as here $a_t=0.5$m/s/s so I just need to find $a_c$ ...in which I am having problem because if the speed of the cyclist was constant I could have easily said $a_c=\frac{v^2}{r}$ but here(in this question)velocity of the cyclist is not constant it is changing with time at the rate of 0.5 m/s/s so I don't think I can directly apply this formula as $v$ is changing here and not constant ...what should I do after this step...any suggestion/help is welcome.


closed as off-topic by Kyle Kanos, Martin, ACuriousMind, Daniel Griscom, Qmechanic Feb 2 '16 at 23:43

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    $\begingroup$ Physics Stack Exchange isn't a homework help site; but, if you do want that kind of help you can take a look at this thread for a list of free online homework help resources. $\endgroup$ – Ulad Kasach Feb 3 '16 at 0:47
  • $\begingroup$ @Vlad K sorry ,but I didn't knew about this ...actually I thought that if there is (homework/exercises )tag available ...then maybe posting a homework question will be fine...sorry again ..will take care next time.. $\endgroup$ – Freelancer Feb 3 '16 at 3:04

The magnitude of centripetal acceleration is $\frac{v^2}{r}$ instantaneously. It applies no matter the speed on your circular path. (Technically it's true for any curve, but $r$ would be changing on non-circular curves, making calculations more difficult.) The tangential acceleration is constant, so you can write a function for $v$. Then you have two mutually perpendicular components of the acceleration vector, one which is constant in magnitude and changing direction (tangential) and the other changing in a calculable fashion as a function of time.

Now set up a coordinate system and use polar coordinates and trigonometry to find the functions of time that tell you the magnitudes and directions of the acceleration components.

Have fun learning!


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