33 33.   A car accelerates from rest at a constant rate $\alpha$ for some time, after which deaccelerates as a constant rate $\beta$ to come to rest. If the total time elapsed is 1, the maximum velocity accquired to the car is given by

Dear student,
Here i am taking a and b in place of

u = 0

= a

t = t s

= b

Let the maximum velocity attained be v at time t1

Thus

v = u + a t1

=> v = at1 ---1.

vf = 0 after t – t1 seconds @ b ms -2  retardation

Thus

0 = v – b(t-t1)

By 1

=> at1 – b(t-t1) = 0

=> t1(a + b) = bt

=> t1 = bt/(a+b)

Again,

v = at1

=> v =  {ab/(a+b)}t
so the final answer will be,

$\left(\frac{\alpha \beta }{\alpha +\beta }\right)t$
Regards

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