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Matter In Our Surroundings

Question
CBSEENSC9005742

If a car moving with 36 km/h increases its speed to 54 km/h in 10 seconds, find (i) acceleration and (ii) distance covered by the car in this time.

Solution
Here comma space space

I n i t i a l space v e l o c i t y space o f space t h e space c a r comma space straight u space equals space 36 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 equals space fraction numerator 36 space cross times space 1000 space straight m over denominator 3600 space straight s end fraction space equals space 10 space straight m divided by straight s

F i n a l space v e l o c i t y comma space straight v space equals 54 space km over straight h space equals fraction numerator 54 space cross times space 1000 space straight m over denominator 3600 space straight s end fraction space equals space 15 space straight m divided by straight s

T i m e space a t space w h i c h space t h e space s p e e d space i n c r e a s e s comma space straight t space equals space 10 space straight s

Acceleration space straight a space equals space ? space space

D i s tan c e space t r a v e l l e d space b y space t h e space c a r space i n space t i m e space t comma space straight s space equals space ?

left parenthesis straight i right parenthesis space U sin g space t h e 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 space

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 15 minus 10 over denominator 10 end fraction space equals space 0.5 space ms to the power of negative 2 end exponent

left parenthesis ii right parenthesis space U sin g space t h e 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 space 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 10 space cross times 10 space plus space 1 half cross times left parenthesis 0.5 right parenthesis space cross times left parenthesis 10 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 straight s space equals space 100 space plus space 25 space equals space 125 space straight m.