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Is Matter Around Us Pure

Question
CBSEENSC9005950

A constant force acts on an object of mass 5 kg for a duration of 2 s. It increases the object’s velocity from 3 ms–1 to 7 ms–1. Find the magnitude of the applied force. Now if the force were applied for a duration of 5 s, what would be the final velocity of the object.

Solution
In space the space first space case colon space

Initial space velocity comma space straight u space equals space 3 space ms to the power of negative 1 end exponent

Final space velocity comma space straight v space equals space 7 space ms to the power of negative 1 end exponent

Time space taken comma space straight t space equals space 2 space straight s

Mass space of space the space body comma space straight m space equals space 5 space kg

Therefore comma space

Acceleration comma space space straight a space equals space fraction numerator straight v minus straight u over denominator straight t 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 equals space fraction numerator 7 minus 3 over denominator 2 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 equals space 4 over 2 space equals space 2 space m s to the power of negative 2 end exponent

Now comma space using space Newton apostrophe straight s space forst space law space of space moton comma space

F o r c e comma space straight F space equals space m a space equals space 5 cross times 2 space equals space 10 space straight N. space
The same force is applied for a duration of 5 s, therefore the acceleration a will remain same.
I n space s e c o n d space c a s e colon

I n i t i a l space v e l o c i t y comma space straight u space equals space 3 space m s to the power of negative 1 end exponent
T i m e space t a k e n comma space straight t space equals space 5 straight s
A c c e l e r a t i o n comma space straight a space equals space 2 space m s to the power of negative 2 end exponent

S o space u s i n 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

space space space space space space space space space straight v space equals space straight u plus a t space

space space space space space space space space space space space space equals space 3 plus 2 cross times 5 space

space space space space space space space space space space space space equals space 13 space m s to the power of negative 1 end exponent. space