QJEEM21Phc549: JEE Main 2021 Physics - Class 11 JEEM21Phc549 Solution: A car accelerates from rest at a constant rate α for some time…

Question

Verified Solution • 2025–26 Session moderate

A car accelerates from rest at a constant rate

α

for some time after which it decelerates at a constant rate

β

to come to rest. If the total time elapsed is t seconds, the total distance travelled is :

Accepted Answer

t_{1} + t_{2} = t,

V^{'} = 0 + α t_{1}

V = u + a t

0 = α t_{1} - β t_{2}

t_{2} = \frac{α}{β} t_{1} = t

t_{1} = (\frac{β}{α + β}) t

Distance

= \frac{1}{2} (t_{1} + t_{2}) \times α t_{1}

(area of triangle)

= \frac{1}{2} t \times α (\frac{β}{α + β}) t

= \frac{α β}{2 (α + β)} t^{2}

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