Question

A car is traveling with a speed of 23.0 m/s along a straight horizontal road. The wheels have a radius of 0.310 m. If the car speeds up with a linear acceleration of 1.30 m/s2 for 8.60 s, find the angular displacement of each wheel during this period.

Answer 1

656.09rad

Step-by-step explanation:

We start from the equation of time based on the acceleration that says the following

`x(t)= (1)/(2)at^2+v_0t+x_0`

We have this values practically,

`v_0=23m/s \\t=8.60s\\a=1.3m/s^2\\x_0 = 0m`

Substituting,

`x(8.6) = (1)/(2)(1.3)(8.6)^2+(23)(8.6)+0\\x(8.6)=203.39m`

Angular velocity is given by,

`d_(\theta)=2\pi*((d)/(2\pi r)) =(d)/(r) = (203.39)/(0.310) = 656.09rad`