Question

The position of a particle moving along the x-axis is given by s(t)=5t2+3. Use difference quotients to find the velocity v(t) and acceleration a(t)."
Since Chegg does not have a solution for this problem, I'd like to check my answers. I got v(t) = 10t and a(t) = 10.

Answer 1

Answer:

$v(t) = 10t$

$a(t) = 10$

Step-by-step explanation:

The velocity is the derivative of the position.

The acceleration is the derivative of the velocity.

In this problem, we have that:

$s(t) = 5t^{2} + 3$

Looking at the derivative table, the derivative of $a*t^{n}$ is $a*n*t^{n-1}$ and the derivative of a constant is 0.

So:

$v(t) = s'(t) = 10t$

$a(t) = v'(t) = 10$

Your answers are correct.