Question

five race - cars speed toward the finish line at the jasper county speedway. the table lists each cars speed in meters/second. if each car has the same mass, which car will require the longest time to come to a full stop?
car a 890 m/s
car b 850 m/s
car c 790 m/s
car d 895 m/s
car e 870 m/s
select the correct answer.
a. car a
b. car b
c. car c
d. car d
e. car e

Explanation:

Step1: Recall the relationship between speed and stopping - time

Assuming the same deceleration for all cars (since each car has the same mass and presumably the same braking - force conditions), the time \(t\) to come to a stop can be related to the initial speed \(v\) using the equation \(v = v_0+at\) (where \(v = 0\) at the stop, \(v_0\) is the initial speed, \(a\) is the deceleration, and \(t\) is the time). Rearranging for \(t\) gives \(t=\frac{v_0}{|a|}\). So, the car with the highest initial speed will take the longest time to come to a stop.

Step2: Compare the speeds of the cars

We are given the speeds of the cars: Car A has a speed of \(890\ m/s\), Car B has a speed of \(850\ m/s\), Car C has a speed of \(790\ m/s\), Car D has a speed of \(895\ m/s\), and Car E has a speed of \(870\ m/s\).
By comparing these values: \(790<850<870<890<895\).

Answer:

D. Car D