Question

A 6.0 kg toy car can move along an x axis; Figure gives Fx of the force acting on the car, which begins at rest at time t=0. The scale on the Fx axis is set by Fxs = 3.0 N. In unit-vector notation, what is p at (a)t = 2.0 s and (b)t = 3.0 s,(c) what is v at t = 7.0 s?

Answer 1

5 units along y axis = 3N ;

1 unit = 3 /5 N

dp = F .dt ;

( a )

p( 2s ) - p ( 0 ) = ∫ F . dt ; t = 0 to t= 2 ,

the RHS is the area under F - t curve from t = 0 to t = 2 s ;

p ( 2s ) - 0 = ( 1 / 2 ) * 2 * ( 3 / 5 ) * 10

p ( 2 s ) = 6 ;

since there is no force along other axes , so the other components of p reamain = 0 ;

p = 6 i + 0 j + 0 k ; kg m /s <-------------ans

( b )

p ( 3 ) - p ( 0 ) = ∫ F . dt ; t = 0 to t= 3 ,

p ( 3 ) - 0 =  ( 1 / 2 ) * 2 * ( 3 / 5 ) * 10 + 1 * ( 3 / 5 ) * 10 ;

p ( 3 ) = 12 ;

p = 12 i + 0 j + 0 k ; kg m /s <-------------ans

( c )

p ( 7 ) - p ( 0 ) = ∫ F . dt ; t = 0 to t= 7 ;

p ( 7 ) - 0 = 2 * ( 1 / 2 ) * 2 * ( 3 / 5 ) * 10 + 2 * ( 3 / 5 ) * 10 - 0.5 * 1 * 5

p ( 7 ) = 29.5 kg m /s ;

m v = 29.5 ;

v = 29.5 / 6 = 4.916 m / s   

v = 4.916 i + 0 j + 0 k m / s <------------ans