(a) Tangential acceleration: [tex]9.5 m/s^2[/tex]
The tangential acceleration is given by:
[tex]a_t = \frac{v-u}{t}[/tex]
where
v = 23 m/s is the final velocity of the car
u = 4 m/s is the initial velocity of the car
t = 2 s is the time taken for the car to accelerate from u to v
Substituting the numbers into the formula, we find
[tex]a_t = \frac{23 m/s-4 m/s}{2 s}=9.5 m/s^2[/tex]
(b) Radial acceleration: [tex]0.49 m/s^2[/tex]
The radial acceleration is equivalent to the centripetal acceleration, which is given by:
[tex]a_r = \frac{v^2}{r}[/tex]
where
v = 16 m/s is the tangential speed
r = 527 m is the radius of the circular orbit
Substituting numbers, we find
[tex]a_r = \frac{(16 m/s)^2}{527 m}=0.49 m/s^2[/tex]
