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Matter In Our Surroundings

Question
CBSEENSC9006320

A car weighing 1000 kg and travelling at 30 mis stops at a distance of 50 m decelerating uniformly. What is the force exerted on it by the brakes? What is the work done by the brakes?

Solution

G i v e n comma space

M a s s space o f space t h e space c a r comma space straight m space equals space 1000 space k g

I n i t i a l space v e l o c i t y comma space straight u space equals space 30 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 space 0

D i s t a n c e space t r a v e l l e d space b y space t h e space c a r comma space straight s space equals space 50 space straight m

U s i n g space 3 to the power of r d end exponent 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 space space space space space space space space straight v squared minus straight u squared space equals space 2 a s
therefore space space space space space space space space space space 0 minus 30 squared space equals space 2 straight a. space 50 space space
rightwards double arrow space space space space space space space space space straight a space equals space minus 900 over 100 space equals negative 9 space straight m divided by straight s squared
 
Therefore comma space
Deceleration space equals space 9 space straight m divided by straight s squared

Decelerating space force comma space straight F space equals ma space equals space 1000 space cross times space 9 space equals space 9000 space straight N.

Work space done space by space the space brakes comma space straight W space equals space straight F. space straight s 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 9000 space cross times space 50 space straight J 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 450000 space straight J.