Answer:
The centripetal acceleration at highway speed is greater.
Explanation:
We assume the motion of the car is uniformly accelerated. Let the highway speed be v.
By the equation of motion,
[tex]v=u+at[/tex]
[tex]a=\dfrac{v-u}{t}[/tex]
u is the initial velocity, a is acceleration and t is time
Because the car starts from rest, u = 0.
[tex]a_T=\dfrac{v}{t}[/tex]
This is the tangential acceleration of the thread of the tire.
The centripetal acceleration is given by
[tex]a_C=\dfrac{v^2}{r}[/tex]
r is the radius of the tire.
Comparing both accelerations and applying commonly expected values to r and t, the centripetal acceleration is seen to be greater. The radius of a tyre is, on the average, less than 0.4 m. Then the centripetal acceleration is about
[tex]a_C=\dfrac{v^2}{0.3}=2.5v^2[/tex]
The tangential acceleration can only be greater in the near impossible condition that the time to attain the speed is on the order of microseconds.
