A car traveling 58.5 km/h is 27.4 m from a barrier when the driver slams on the brakes. The car hits the barrier 2.18 s later. (a) What is the car's constant deceleration magnitude before impact? (b) How fast is the car traveling at impact ?

Question

Sebastian Acosta · Accepted Answer

#a = -"3.38 m/s"""^2#
#v_"impact" = "8.88 m/s"# First, change the vehicle's starting speed from kilometers per hour to meters per second. #58.5color(red)(cancel(color(black)("km")))/color(red)(cancel(color(black)("h"))) * (1color(red)(cancel(color(black)("h"))))/(60color(red)(cancel(color(black)("min")))) * (1color(red)(cancel(color(black)("min"))))/(60color(red)(cancel(color(black)("s")))) * "1000 m"/(1color(red)(cancel(color(black)("km")))) = "16.25 m/s"# Assuming that the car stays in the same direction of travel, its velocity and speed will be equal. Thus, you are aware that the car is traveling at 16.25 m/s when it starts to break and that it required 2.18 seconds for it to travel 27.4 meters at a constant slow speed. Thus, you are able to write. #color(blue)(d = v_0 * t + 1/2 * a * t^2)" "#, where #d# - the distance to the barrier; #v_0# - the initial speed of the car; #t# - the stopping time; #a# - the deceleration - you can expect it to be negative; When a car slows down, its acceleration vector will be oriented in the opposite direction of its motion, so you can expect the acceleration to be negative if the direction of motion is taken to be positive. Rearrange this equation to solve for #a# #d = v_0 * t = 1/2 * a * t^2# #a = (2 * (d - v_0 * t))/t^2# #a = (2 * (27.4"m" - 16.25"m"/color(red)(cancel(color(black)("s"))) * 2.18color(red)(cancel(color(black)("s")))))/(2.18^2 "s"""^2) = color(green)(-"3.38 m/s"""^2# Use the equation to find the car's speed when it collides. #color(blue)(v_"impact" = v_0 + a * t)" "#, where #v_"impact"# - the speed upon impact; Enter your values to obtain #v_"impact" = 16.25"m"/"s" + (-3.38)"m"/"s"^color(red)(cancel(color(black)(2))) * 2.18color(red)(cancel(color(black)("s"))) = color(green)("8.88 m/s")#

Layla Ahmed · Answer

undefined (a) The car's constant deceleration magnitude before impact is $ 5.34 \, \text{m/s}^2 $. (b) The car is traveling at $ 43.3 \, \text{km/h} $ at impact.