Starting from rest, a car accelerates down a straight road with constant acceleration a 1 for a time t 1 , then the acceleration is changed to a different constant value a 2 for an additional time t 2 . The total elapsed time is t 1 + t 2 . Can the equations of kinematics be used to find the total distance traveled?

Question

Starting from rest, a car accelerates down a straight road with constant acceleration  a 1  for a time  t 1 , then the acceleration is changed to a different constant value  a 2  for an additional time  t 2 . The total elapsed time is  t 1  +  t 2 . Can the equations of kinematics be used to find the total distance traveled?

Answer

No, because this is not a case of constant acceleration.

Answer

Yes, use  a 1  +  a 2  as the acceleration and the average time ( t 1  +  t 2 )/2 in the calculation.

Answer

Yes, break the problem up into 2 problems, one with the conditions for the first time interval and the other with the conditions for the second time interval, noting that for the second time interval the initial velocity is that from the end of the first time interval. When done, add the distances from each of the time intervals.

Answer

Yes, use ( a 1  +  a 2 )/2 as the average acceleration and the total time in the calculation.

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Starting from rest, a car accelerates down a straight road with constant acceler...

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