Question

A roller coaster car moves around a vertical circle. At the bottom of the circle, the car experiences four times as much radial (centripetal) acceleration as at the top of the circle. Compared to its speed at the top of the circle, the speed of the car at the bottom of the circle is:
A. four times as great.
B. 16 times as great
C. √2 times as great
D. twice as great
E. 2√2 times as great.

Answer 1

Answer:

The speed of the car at the bottom of the circle is twice as its speed at the top of the circle.

Explanation:

It is given that, at the bottom of the circle, the car experiences four times as much radial (centripetal) acceleration as at the top of the circle such that :

$a_B=4\times a_T$

The centripetal acceleration is given by :

$a=\dfrac{v^2}{r}$

Let $v_B\ and\ a_T$ are the speed of the roller coaster car at bottom and at top respectively.

$\dfrac{a_B}{a_T}=4\\\\\dfrac{(v_B^2/r)}{(v_T^2/r)}=4\\\\\dfrac{v_B^2}{v_T^2}=4\\\\\dfrac{v_B}{v_T}=2\\\\v_B=2\times v_T$.

So, the speed of the car at the bottom of the circle is twice as its speed at the top of the circle. Hence, the correct option is (D).