A car accelerates from rest at a constant rate A for some time after which it retards at constant rate - Physics - Motion In A Straight Line

Question

A car accelerates from rest at a constant rate A for some time
after which it retards at constant rate B to come to rest If the
total time lapse is T seconds, evaluate the maximun velocity
reached and total distance travelled, in terms of A, B and T

Hansraj Rai · Accepted Answer

Dear Student!! Let t and t' are the time of acceleration and deceleration respectively Let v be max velocity

$t + t' = T \frac{v}{t} = A, \frac{v}{t'} = B S o, t + t' = \frac{v}{A} + \frac{v}{B} = T T = v (\frac{A + B}{A B}) v = (\frac{A B}{A + B}) T$ Total distance traveled = Area under v-t graph $= \frac{1}{2} (t + t') v = \frac{1}{2} T v = \frac{1}{2} (\frac{A B}{A + B}) T^{2}$

A car accelerates from rest at a constant rate A for some time after which it retards at constant rate B to come to rest. If the total time lapse is T seconds, evaluate the maximun velocity reached and total distance travelled, in terms of A, B and T