Question

After t seconds the displacement, s(t), of a particle moving rightwards along the x-axis is given (in feet) by

s(t) = 4t^2-5t+3

By determining the average velocity
successively over the time intervals
[1, 1.1], [1, 1.01],

what is a plausible estimate for the instantaneous velocity, v(1), of
the particle at time t = 1.

ANSWER CHOICES:

1. v(1) = 3 ft/sec
2. v(1) = 1 ft/sec
3. v(1) = 4 ft/sec
4. v(1) = 5 ft/sec
5. v(1) = 2 ft/sec

Answer 1

`v(1) = 2\ ft/s`

Explanation:

Given

`s(t) = 4t^2-5t+3`

Required

Determine the instantaneous velocity at
`t = 1`

First, we need to determine s(1)

`s(t) = 4t^2-5t+3`

`s(1) = 4(1)^2 - 5(1) + 3`

Evaluate all brackets

`s(1) = 4*1 - 5*1 + 3`

`s(1) = 4 - 5 + 3`

`s(1) = 2`

Next; v(t) is calculated as thus;

`v(t) = (s(t))/(t)`

Substitute 1 for t

`v(1) = (s(1))/(1)`

Substitute 2 for s(t)

`v(1) = (2)/(1)`

`v(1) = 2\ ft/s`