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Matter In Our Surroundings

Question
CBSEENSC9005743

A train starting from rest attains a velocity of 72 km/h in 5 minutes. Assuming that the acceleration is uniform, find (i) the acceleration and (ii) the distance travelled by the train for attaining this velocity.

Solution
G iven space straight a space train space starts space from space rest.

So comma space initial space velocity space equals space 0

Time space of space travel comma straight t space equals space 5 space min space equals space 300 space straight s

V e l o c i t y space a t t a i n e d space b y space t h e space t r a i n comma space straight v space equals space 72 space km over straight h

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 72 space cross times space 1000 space straight m over denominator 3600 space straight s end fraction
space
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 20 space straight m divided by straight s

left parenthesis straight i right parenthesis space U sin g space f i r s t space e q u a t i o n space o f space m o t i o n comma

Acceleration comma space space space straight a space equals space fraction numerator straight v minus straight u over denominator straight t end fraction space equals space fraction numerator 20 minus 0 over denominator 300 end fraction space equals space 1 over 15 straight m divided by straight s. space

left parenthesis ii right parenthesis space U sin g space s e c o n d space e q u a t i o n space o f space m o t i o n comma
Distance space t r a v e l l e d comma space straight s space equals space ut plus space 1 half at squared space
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 0 space cross times space 300 plus space 1 half cross times 1 fifth cross times left parenthesis 300 right parenthesis squared
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 3000 space straight m space equals space space 3 space km.