A car is initially at rest on a straight road. The histogram below shows the car

Question

A car is initially at rest on a straight road. The histogram below shows the car's acceleration along that road as a function of time :-....:-... 8 1 2 3 4 5 6 7 8 9 18 11 12 13 14 Time (s) Calculate the speed of the car att 3 s 6.00 m/s You are correct. Your receipt no. is 169-7865 Calculate the distance traveled during the first 6 s 29 m Submit Answer Incorrect. Tries 1/20 Previous Tries Calculate the distance traveled from t-10 s to t-13s Tries 0/20 Submit Answer Calculate the car's average speed from t = 5 s to t=9 s

Explanation / Answer

i] Initial velocity = 0 m/s

then from t = 1s to t = 3s, a = 3 m/s2

so, D = 0 + (1/2)at2 = 6 m

and v = 0 + 3(2) = 6 m/s

from t = 3s to t = 4s, a = 2 m/s2

so, D = 6 + 6(1) + (1/2)at2 = 13 m

and v = 6 + 2(1) = 8 m/s

from t = 4s to t = 6s, a = - 2 m/s2

therefore, D = 13 + 8(2) - (1/2)(2)(2)2 = 25 m

this is the distance traveled in the first 6 seconds.

ii] To find the distance traveled from t=10s to t=13s, determine the speed at t = 10s

this is v = 6 m/s and acceleration = 0 m/s2 from t = 10s to t = 13s.

so, distance traveled is: D = 6(13 - 10) = 18 m.

iii] Average speed from t = 5s to t = 9s is:

vavr = (x(9) - x(5))/(9 - 5).

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