contestada

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

Respuesta :

MrRoyal

Answer:

[tex]v(1) = 2\ ft/s[/tex]

Step-by-step explanation:

Given

[tex]s(t) = 4t^2-5t+3[/tex]

Required

Determine the instantaneous velocity at [tex]t = 1[/tex]

First, we need to determine s(1)

[tex]s(t) = 4t^2-5t+3[/tex]

[tex]s(1) = 4(1)^2 - 5(1) + 3[/tex]

Evaluate all brackets

[tex]s(1) = 4*1 - 5*1 + 3[/tex]

[tex]s(1) = 4 - 5 + 3[/tex]

[tex]s(1) = 2[/tex]

Next; v(t) is calculated as thus;

[tex]v(t) = \frac{s(t)}{t}[/tex]

Substitute 1 for t

[tex]v(1) = \frac{s(1)}{1}[/tex]

Substitute 2 for s(t)

[tex]v(1) = \frac{2}{1}[/tex]

[tex]v(1) = 2\ ft/s[/tex]

Otras preguntas