# Thread: Motion along a straight line question

1. ## Motion along a straight line question

A particle moves from fixed pt. O along a straight line. It's velocity v m/s, t s after passing through O is given by v=4t-5. Find the total distance traveled by the particle when t=3. The answer is 48.25m. Any help? This book has lots of error-ed answers, so I'm not really sure..

2. Originally Posted by smmxwell
A particle moves from fixed pt. O along a straight line. It's velocity v m/s, t s after passing through O is given by v=4t-5. Find the total distance traveled by the particle when t=3. The answer is 48.25m. Any help? This book has lots of error-ed answers, so I'm not really sure..
I do not agree with the "answer". assuming that the question is asking for total distance traveled from t = 0 to t = 3 ...

particle is moving left from t = 0 to t = 5/4 sec

distance traveled in that interval = (1/2)(5/4)(5) = 25/8 m

from t = 5/4 to t = 3 sec, the particle moves to the right ...

distance traveled in that interval = (1/2)(7/4)(7) = 48/8 m

total distance traveled = 25/8 + 49/8 = 74/8 = 9.25 m

total distance can also can be calculated by the definite integral ...

$\int_0^3 |4t-5| \, dt$

3. Thanks. Guess my anwser was correct all along.