An air bag applies a force of 6100 N to bring about a change in momentum of 3540 kg m/s. How much time did it act over
A. 0.26 s
B. 6.1 s
C. 0.58 s
D. 35 s
E. 1.7 s
In fact, Newton's second law says that the force applied to an object is the product between the mass and the acceleration of the object: [tex]F=ma[/tex] but the acceleration is the change of velocity in a time [tex]\Delta t[/tex]: [tex]a= \frac{\Delta v}{\Delta t} [/tex] So F becomes [tex]F=m \frac{\Delta v}{\Delta t} [/tex] Remembering that the momentum is the product between mass and velocity: [tex]p=mv[/tex] The numerator in the formula of F is the change in momentum: [tex]F= \frac{\Delta p}{\Delta t} [/tex] So we can find the interval of time the force acts: [tex]\Delta t= \frac{\Delta p}{F}= \frac{3540 kg m/s}{6100 N}=0.58 s [/tex]
