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Motion In Straight Line

Question
CBSEENPH11017185

A car starts from rest and accelerates uniformly. After n seconds, it acquires the speed v. Find the distance travelled by the car in last 2s.

Solution

Given that,
Initial velocity, u = 0
Acceleration, a = ?
At  t = n, the velocity of particle is v is given by the first equation of motion. 
therefore space straight nu space equals space 0 space plus space an
rightwards double arrow   space space straight a space equals space straight v over straight n
Velocity of car at t = n - 2 is given by,
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Now, the distance tracvelled by the car in last two second is,
straight S equals 2 straight V plus 1 half straight alpha open parentheses 2 close parentheses squared
space space space equals 2 straight v over straight n left parenthesis straight n minus 2 right parenthesis plus 1 half straight v over straight n 4

space space space space equals space fraction numerator 2 left parenthesis straight n minus 1 right parenthesis straight v over denominator straight n end fraction