Question

a car speed uniformly from rest until it reaches the velocity 15m/s in 20s . the tyre radius in 0.3m . calculate the angular acceleration and number of rotations during that time.

Answer 1

$v=at\to a=v/t=15/20=0.75(m/s^2)$

$s=v^2/(2a)=15^2/(2\cdot0.75)=150(m)$

$n=150/(2\cdot3.14\cdot0.3)=79.58$

$\phi=\epsilon\cdot t^2/2\to \epsilon=2\cdot\phi/t^2=$

$=2\cdot79.58\cdot2\cdot3.14/15^2=2.5(rad/s^2)$

Answer. $\epsilon=2.5(rad/s^2);n=79.58$