Question

A motorcar of mass `1200kg` is moving along a straight line with a uniform velocity of `90 km//h`. Its velocity is slowed down to `18 km//h` in `4s` by an unbalanced external force. Calculate the acceleration and change in momentum. Also, calculate the magnitude of the force required.

Answer 1

(a) Calculation of acceleration
Here, Initial velocity,u=90km/h
`=(90xx1000m)/(60xx60s)`
=25 m/s
Final velocity,v=18 km/h ltbr? `=(18xx1000m)/(60xx60s)`
=5m/s
Acceleration,a=? (To be calculated)
And, Time,t=4s
Now, v=a+ut
`5=25+axx4`
4a=5-25
4a=-20
`a=-20/4`
`a=-5m//s^(2)`
Thus, the acceleration of the motorcar is, `-5 m//s^(2)`. It is actually negative acceleration or retardation.
(b) Calculation of change in momentum
Change in momentum =mv-mu
`=1200xx5-1200xx25`
`=6000-30000`
`=-24000kg.m//s`
Thus, the change in momentum is 24000 kg. m/s
(c) Calculation of magnitude of force
Force, F=`mxxa`
`F=1200xx(-5)`
F=-6000N
Thus, the magnitude of force required is 6000 newtons. The negative sign shows that this force is opposing the motion.