Question

as possible or the centripetal acceleration at highway speed? For the tread on your car tires, which is greater: the tangential acceleration when going from rest to highway speed as quickly as possible or the centripetal acceleration at highway speed? The centripetal acceleration at highway speed is greater. The tangential acceleration when going from rest to highway speed as quickly as possible is greater. Under different realistic conditions the answer can be either acceleration.

Answer 1

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,

$v=u+at$

$a=\dfrac{v-u}{t}$

u is the initial velocity, a is acceleration and t is time

Because the car starts from rest, u = 0.

$a_T=\dfrac{v}{t}$

This is the tangential acceleration of the thread of the tire.

The centripetal acceleration is given by

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

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

$a_C=\dfrac{v^2}{0.3}=2.5v^2$

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.