Analyze Evaluate the initial and final momenta of the car: P_i = mv_i = (1, 500

Question

Analyze Evaluate the initial and final momenta of the car: P_i = mv_i = (1, 500 kg)(-16.5 i m/s) P_f = mv_f = (1, 500 kg)(2.35 i m/s) Find the impulse on the car: I = Delta P = P_f - P_i Evaluate the average force exerted by the wall on the car: (sigma F)_avg = I/Delta t = Delta p/0.195 s Notice that the signs of the velocities in this example indicate the reversal of directions. What would the mathematics be describing if both the initial and final velocities had the same sign? Now in real life, this automobile is cruising at 21.5 m/s (equal to 77.4 km/hr) when it is about to hit a pedestrian stuck in the middle of the road. The super hero Mr. Incredible comes to the rescue. He does not want to get sued, however. Therefore, he will not push the car with a force greater than 2.0 times 10^4 N, otherwise, the bumper will get damaged. How much time does he need to stop this car?

Explanation / Answer

given
vi = 21.5 m/s

vf = 0

acceleration of the car,

a = -F/m

= -2*10^4/1500

= -13.33 m/s^2

let t is the time taken.

now use, vf = vi + a*t

==> t = (vf - vi)/a

= (0 - 21.5)/(-13.33)

= 1.61 s

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