Write down the comprehensive expression for the force of a particle of particle

Question

Write down the comprehensive expression for the force of a particle of particle of variable mass m kilograms moving with a velocity (v) and contrast this to the generally accepted equation F = ma A vehicle decelerates at a rate of -2t m/s/s, where t is. the time in seconds. if the initial velocity of the vehicle is m/s, what is the elapsed time before the vehicle comes to a stop. A sport drag racing car starts from rest and accelerates for 3 seconds at a uniform rate of 40 m/s/s at the end of which time the car maintains the speed achieved until it decelerates to zero speed in two (2) seconds and then stops at the 1000 meter finish line. (Draw the velocity-time curve and specify what the area under the velocity time curve indicates) How long in seconds, did it take the car to finish the race? What is the constant speed achieved? What is the final deceleration of the drag racing car? If the 1000 meter world record is 9.64 seconds, has the world record been broken?

Explanation / Answer

5b ) a= -2 t m/s^2

v = 100 m/s

a= dv/dt

adt = dv

(-2t) dt = dv

intergetating on both sides

-t^2 = v

plugging limits

-t^2 = 0 - 100

t = 10 sec ( time )

Q.6 , u = 0 t= 3 seconds, a= 40 m/s^2,, v = at = 120 m/s

Final v= 0 , a( retardation) = 120/ 2 = - 60 m/s^2, distance = 1000 m

a) distance covered during acceleration= 0.5 ( 40) ( 3)^2= 180 m

distance covered during decelerating = 120 ( 2) - 0.5 ( 60) ( 2)^2 = 120 m

remaining distance = ( 1000 - 300 ) = 700 m covered at a speed of 120 m/s = 5.833 seconds

Total time= 10.833 seconds apprx

b)consatnt speed = 120 m/s

c)final decleration= -60 m/s^2

d) No record has not been broken

d)

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