a bus moves from rest with a uniform acceleration of 2ms² for the first 10 seconds. it then accelerate at a uniform rate of 1ms² for another 15seconds. it continues at a constant speed for 70seconds and finally came to rest in 20seconds by uniform acceleration. calculate the average retardation as the body is brought to rest
v1=a1t1=20 ms.v_1=a_1t_1=20~\frac ms.v1=a1t1=20 sm.
s1=a1t122=100 m.s_1=\frac{a_1t_1^2}{2}=100~m.s1=2a1t12=100 m.
v2=v1+a2t2=20+15=35 ms.v_2=v_1+a_2t_2=20+15=35~\frac ms.v2=v1+a2t2=20+15=35 sm.
s2=v1t2+a2t222=300+112.5=412.5 m.s_2=v_1t_2+\frac{a_2t_2^2}{2}=300+112.5=412.5~m.s2=v1t2+2a2t22=300+112.5=412.5 m.
s3=v2t3=2450 m.s_3=v_2t_3=2450~m.s3=v2t3=2450 m.
a3=v2t4=1.75 ms2.a_3=\frac{v_2}{t_4}=1.75~\frac{m}{s^2}.a3=t4v2=1.75 s2m.
s4=a3t422=350 m.s_4=\frac{a_3t_4^2}{2}=350~m.s4=2a3t42=350 m.
s=s1+s2+s3+s4=3312.5 m.s=s_1+s_2+s_3+s_4=3312.5~m.s=s1+s2+s3+s4=3312.5 m.
t=t1+t2+t3+t4=115 s.t=t_1+t_2+t_3+t_4=115~s.t=t1+t2+t3+t4=115 s.
v=st≈28.8 ms.v=\frac st\approx 28.8~\frac ms.v=ts≈28.8 sm.
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