-1
$\begingroup$

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.

$\endgroup$

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

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – Kyle Kanos, Martin, ACuriousMind, Daniel Griscom, Qmechanic
If this question can be reworded to fit the rules in the help center, please edit the question.

  • 1
    $\begingroup$ 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
1
$\begingroup$

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!

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.