If x=t^3 - 4t^2 - 3t then find the distance traveled from t=0 to t=4s.
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Given:
x=t^3 - 4t^2 - 3t
To find:
The distance traveled from t=0 to t=4s.
Calculation:
Since the question asks for "distance" and not "displacement" , we need to first check that if the body has stopped and changed its direction of motion in the given time interval.
Now, put v = 0 , to check if the car stopped.
So, t = 3 sec , at which the car stopped.
In that case, first we need to calculate the position at t = 3 sec and t = 0 sec and t =4 sec.
At t = 0 sec ,
At t = 4 sec,
So, the particle move in the sequence as follows:
- At t = 0 , it was at 0 m position.
- At t = 3 sec , it was at -18 m position, and it stopped and changed its direction (travelled 18 m)
- At t = 4 sec , it is at -12 m position. (travelled 6 metres from -18 m position).
So, net distance will be :
So, particle travelled for 24 metres in the given time interval.
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