Radius of car= 70m,travelling with speed=120 km/h= 120×185=33.33sm ,
acceleration=4m/s2, time=t=4s,
we take inital position of particles as
x=rcosθi+rsinθj,
v=−rωsinθi+rωcosθj
and
acceleration
a=−r(ω2cosθ+αsinθ)i+r(ω2sinθ+αcosθ)j
Now, we know that initially angle θ=0o
vi= rωi , ωi=7033.33=0.476rad/s
Now, after time t= 4 ,
ωf=7016+33.33=0.7047rad/s
α=4ωf−ωi=0.057s2rad
this is angular acceleration of car
θ=ωit+0.5αt2=0.476×4+0.5×0.057×16=135.286o
this is the angular dispalcement of car after 4 second
Now,
Vf=−70×.7047sin(135.286)i+70×0.7047cos(135.286)j
Vf =−34.706i−35.054j
So here x component of velocity will be vx= -34.706 m/s and y component of velocity is vy= 35.054 m/s
Now acceleration of particles will be
a=−70(0.70472cos(135.285)+0.057sin(135.286)i+70(0.70472sin(135.286)+0.057cos(135.286))j
a=-21.89 i- 21.89j
a=30.96 m/s2
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