Question

The position x of a particle w.r.t. time t along x–axis is given by x = 9t2
– t3
where x is in metre and t
in second. Find
(a) Maximum speed along +x direction
(b) Position of turning point
(c) Displacement in first ten seconds
(d) Distance travelled in first ten seconds

Answer 1

Answer:

(a) = 27m/s

(b) = 108m

(c) = (-100)m

(d) = 316m

Explanation:

Here's the explanation of (d):

We know that distance is the magnitude of displacement and is always positive. And as we know the turning point already, we can seperate both of them and individually so that it remains positive. For doing so, integrate x with limits 0 to 10. Since we know the turning point, seperate them in two different integrations. Change the sign of the second integration to make it positive. Now solve and you will get the answer in next 3-4 steps.

[Note]- I'm also a student and has started learning these things from a very few days so I can also be wrong. Please cross check the answers, especially the last one.

Answer 2

Explanation:

for maximum speed velocity is 0

at turning point velocity is 0