Answer:
The transverse component of acceleration is 26.32 [tex]m/s^2[/tex] where as radial the component of acceleration is 8.77 [tex]m/s^2[/tex]
Explanation:
As per the given data
u=π/4 rad
ω=u'=2 rad/s
α=u''=4 rad/s
[tex]r=e^u[/tex]
So the transverse component of acceleration are given as
[tex]a_{\theta}=(ru''+2r'u')\\[/tex]
Here
[tex]r=e^u\\r=e^{\pi/4}\\r=2.1932 m[/tex]
[tex]r'=e^u.u'\\r'=2.1932 \times 2\\r'=4.3864 m[/tex]
So
[tex]a_{\theta}=(ru''+2r'u')\\a_{\theta}=(2.1932\times 4+2\times 4.3864 \times 2)\\a_{\theta}=26.32 m/s\\[/tex]
The transverse component of acceleration is 26.32 [tex]m/s^2[/tex]
The radial component is given as
[tex]a_r=r''-r\theta'^2[/tex]
Here
[tex]r''=e^u.u'^2+e^u u''\\r''=2.1932 \times (2)^2+2.1932\times 4\\r''=17.5456 m[/tex]
So
[tex]a_r=r''-ru'^2\\a_r=17.5456-2.1932\times (2)^2\\a_r=8.7728 m/s^2[/tex]
The radial component of acceleration is 8.77 [tex]m/s^2[/tex]
