Answer:
a. [tex]12.3m/s^{2}[/tex]
b. [tex]21.93m/s^{2}[/tex]
Explanation:
From the data given, the radius is 5.0m, and the time taken to complete one circle is 4.0secs
Since the motion is in a circular part, we can conclude that the total distance covered in this time is given as circumference of the circle.
which is expressed as
[tex]Distance=2\pi R[/tex]
To determine the speed, we use the equation
[tex]speed=\frac{distnce}{time}\\ Speed=\frac{2\pi R}{time}\\ speed=\frac{2\pi*5 }{4}\\ Speed=7.85m/s[/tex]
The acceleration as required is expressed as
[tex]a=\frac{v^{2}}{r}\\ a=\frac{7.85^{2}}{5}\\ a=12.3m/s^{2}[/tex]
if the speed increase and it takes 3secs to complete one circle, the speed is
[tex]speed=\frac{distnce}{time}\\ Speed=\frac{2\pi R}{time}\\ speed=\frac{2\pi*5 }{3}\\ Speed=10.47m/s[/tex]
and the acceleration becomes
[tex]a=\frac{v^{2}}{r}\\ a=\frac{10.47^{2}}{5}\\ a=21.93m/s^{2}[/tex]
