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# Answer to Question #11477 in Mechanics | Relativity for jo

Question #11477
a car accelerates from rest at a constant rate a for sometime after which it decelerates at a constant rate b to come to rest .if the total time elapsed is t second evaluate a)the max. velocity b)the total distance travelled
Let&#039;s denote Ta the acceleration time of a car and Td the deceleration time. Then

a&middot;Ta = |b|&middot;Td

Also we know that

Ta + Td = T.

So,

Td = T - Ta = a&middot;Ta/|b| ==&gt; Ta(a/|b|+1) = T ==&gt; Ta = T/(a/|b|+1),

and the maximum velocity of a car is

Vmax = a&middot;T/(a/|b|+1).

The total travelled distance is

D = Da + Dd = a&middot;Ta&sup2;/2 + b&middot;Td&sup2;/2 = a&middot;Ta&sup2;/2 + b&middot;(T-Ta)&sup2;/2 = a&middot;(T/(a/|b|+1))&sup2;/2 + b&middot;(T-T/(a/|b|+1))&sup2;/2

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