Question
During an automobile crash test, the average force exerted by a solid wall on a 2500-kg car that hits the wall is measured to be 740,000 N over a 0.22-s time interval. What was the initial speed of the car prior to the collision, assuming the car is at rest at the end of the time interval?
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Solution video
OpenStax College Physics for AP® Courses, Chapter 8, Problem 8 (Test Prep for AP® Courses)
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This is College Physics Answers with Shaun Dychko. This car is approaching a wall during a crash test and has some speed that we want to figure out and we know that the wall is exerting a force of 740000 newtons on the car, the car has a mass of 2500 kilograms and it's in contact with the wall for 0.22 seconds before coming to rest and the question is what is its initial speed? So net force is just the force f applied on the car due to the wall—there's only one horizontal force— and it's going to equal the change in momentum divided by change in time so that's mass times the final velocity minus mass times initial velocity over time— the final velocity being zero— and so we have negative mv i over Δt is the force. And we can multiply both sides by Δt here and then also divide both sides by negative m and we get the initial speed: it's the force times the time divided by negative mass. So that's negative 740000 newtons and I put a negative in front of that because it's pointing to the left and our coordinate system has positive to the right times 0.22 seconds divided by negative 2500 kilograms and that is positive 65 meters per second and we expected positive since the car's initially moving to the right. And... there we go!