Question

A position of a particle moving on an x axis is given by x=7•4 + 9•2t - 2•1 t^3, with x in meters and t in seconds. what is its velocity at t=3•5s? is the velocity,or is it Continuously changing?​

Answer 1

The velocity at that time would be
`(-67.975\; \rm s)`. The velocity of this particle is continuously changing.

Step-by-step explanation:

Differentiate the expression for position
`x` with respect to time
`t` to find an expression for velocity.

`\begin{aligned}v(t) &= (d)/(dt)[x(t)] \\ &= (d)/(dt) \left[ 7.4 + 9.2\, t - 2.1\, t^(3)\right]\\ &= 9.2 - 6.3\, t^(2)\end{aligned}`.

Hence, at
`t = 3.5\; \rm s`, velocity would be
`v(3.5) = 9.2 - 6.3 * (3.5)^(2) = -67.975\; \rm m`.

Since velocity
`v(t)` changes with time
`t`, the velocity of this particle is continuously changing.