Question

A car with tires of radius 25.0 cm accelerates from rest to 30.0 m/s in 10.0 s. When the car's speed is 2.00 m/s find the linear acceleration of the top of the wheel relative to (a) the center of the wheel, (b) the road. (Note that there will be a vertical and horizontal component to the acceleration.

Answer 1

given,

radius of tire = 25 cm = 0.25 m

initial velocity = 0 m/s

final velocity = 30 m/s

time = 10 s

a) acceleration with respect to center

v = u + a t

30 = 0 + 10 a

a = 3 m/s²

radial acceleration

`a_r = (v^2)/(r)`

`a_r = (2^2)/(0.25)`

`a_r =16\ m/s^2`

`a=√(a_r^2 + a_t^2)`

`a=√(16^2 + 3^2)`

`a=16.28\ m/s`

acceleration w.r.t center of tire =
`a=16.28\ m/s`

b) acceleration with respect to road will be equal to 3 m/s²