Question

Part A Express your ansre usinwsonn fo Part B t the car contnss to decelerate at this rate, how much more time is required for it to stop? Express your anseer to two significent figures and Include the appropriate units. lfthe car co thues to decelerate ล'this rate, how far does it go? Find the total dstance

Answer 1

a)

Given

V_o = 86 Km/h =86*1000/3600 =23.89 m/s

V=59*1000/3600 =16.39 m/s

radius

r=d/2 =0.82/2 =0.41 m

angular speed

W_o=V_o/r =23.89/0.41=58.2656 rad/s

W=V/r =16.39/0.41 =39.973 rad/s

From

$\omega ^{2}=\omega _{o}^{2}+2\alpha \Delta \theta$

$39.973^{2}=58.2656^{2}+2\alpha \times (95\times 2\pi )$

$\alpha =-1.5053 rad/s^{2}$

b)

From

$\omega =\omega _{o}+\alpha t$

39.973 =58.2656+(-1.5053)t

t=12.15 s

c)

angular displacement before the car stops ,when the car stops final angular speed is zero i.e W=0

$0 =58.2656^{2}+2(-1.5053)\Delta \theta$

$\Delta \theta =1127.64 rad$

Total linear displacement

$X=r\Delta \theta =0.41\times 1127.64=462.33 m$