Question #a7378

1 Answer
Oct 24, 2016

Answer:

(b)

Explanation:

The car accelerates from rest with an acceleration of # alpha# for a time #t_1#.
velocity after time #t_1# is given by the expression
#v=u+at#
Inserting given values we have
#v=0+alphat_1#
#=>v=alphat_1# .......(1)
Thereafter it is decelerated at a rate #beta# for a time #t_2# when it comes to halt.
We have
#0=v-betat_2#
#=>v=betat_2# .....(2)
Total time #t_1+t_2=t#
#=>t_2=t-t_1#
Inserting in (2) we get
#v=beta(t-t_1)# ......(3)
From (1) we have #t_1=v/alpha#. Inserting in (3) above
#v=beta(t-v/alpha)#

Solving for #v#, we have

#v+beta/alphav=betat#
#=>v(1+beta/alpha)=betat#
#=>v=(betat)/(1+beta/alpha)#
#=>v=(alphabetat)/(alpha+beta)#