The answer is option (B) 1300 N. The airbag exerts a force of magnitude 1300 N on the driver.
Given that initially, the car travels with a velocity of 22 m/s. We have to consider the fact that the velocity of the car and the driver is the same.
- ie, the initial velocity of the driver is [tex]u=22\,m/s[/tex].
The car meets with an accident bringing its velocity down to zero.
- ie, the final velocity of the driver is [tex]v=0\,m/s[/tex]
The car is brought to a stop in 1.4 s.
- ie, the time taken to stop the car is [tex]t=1.4\,s[/tex].
- We know that, [tex]acceleration =\frac{change \:in \:velocity}{time\:taken}[/tex]
- ie, [tex]a=\frac{v\,-\,u}{t} [/tex]
Substituting the given values, we get;
- [tex]a=\frac{0\,m/s\,-\,22\,m/s}{1.4\,s} =-15.71\,m/s^2[/tex]
- Here, the acceleration is negative. That means the driver undergoes deceleration.
Now, from Newton's second law of motion,
[tex]F=ma[/tex]
Substituting the values for the driver's mass and acceleration, we get;
[tex]F= (81\,kg )\times \,(-15.71\,m/s^2)=-1272.51\,N[/tex]
The negative sign indicates the direction of the force exerted. It will be opposite to the motion of the car.
Hence the magnitude of the force is obtained as 1272.51 N. In case the closest option given here is 1300 N. The answer can be approximated to 1300 N.
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