Josh Sizemore

2021-12-26

Suppose that the position of a particle is given by

(a) Find the velocity at time t.

(b) Find the velocity at time

_____

(c) Find the acceleration at time t.

(d) Find the acceleration at time

_____

Thomas Lynn

Beginner2021-12-27Added 28 answers

Step 1 Given

Position of a particle is given by$s\left(t\right)=4{t}^{3}+5t+9$

Step 2 (a) Velocity at time t

Given: Position$s\left(t\right)=4{t}^{3}+5t+9$

Velocity$v\left(t\right)$ is given by: $v\left(t\right)=\frac{d\left[s\left(t\right)\right]}{dt}$

$v\left(t\right)=\frac{d\left[s\left(t\right)\right]}{dt}$

$v\left(t\right)=\frac{d(4{t}^{3}+5t+9)}{dt}$

$4\left(3\right){t}^{3}-1+5\left(1\right)+0$

$=12{t}^{2}+5$

Therefore, velocity at time t is:$v\left(t\right)=(12{t}^{2}+5)\frac{m}{s}$

Position of a particle is given by

Step 2 (a) Velocity at time t

Given: Position

Velocity

Therefore, velocity at time t is:

Joseph Lewis

Beginner2021-12-28Added 43 answers

Step 3 (b) Velocity at time $t=3$ seconds

Velocity at time t is:$v\left(t\right)=12{t}^{2}+5$

Therefore, velocity at time$t=3$ seconds is given by

$v\left(t\right)=12{t}^{2}+5$

$v\left(3\right)=12{\left(3\right)}^{2}+5$

$=12\left(9\right)+5$

$=108+5$

$=113$

Therefore, velocity at time$t=3$ seconds is:

$v=113\frac{m}{s}$

Velocity at time t is:

Therefore, velocity at time

Therefore, velocity at time

karton

Expert2022-01-09Added 613 answers

Step 4 (c) Acceleration at time t

Velocity at time t is:

Acceleration a(t) is given by:

=24t

Therefore, acceleration at time t is:

Step 5 (d) Acceleration at time t=3 seconds

Acceleration at time t is: a(t)=24t

Therefore, acceleration at time t=3 seconds is given by

a(t)=24t

a(3)=24(3)

=72

Therefore, acceleration at time t=3 seconds is:

xleb123

Skilled2023-06-19Added 181 answers

Andre BalkonE

Skilled2023-06-19Added 110 answers

22+64

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