# Acceleration and velocity involving calculus

1. Sep 25, 2006

### needhelp83

If the equation describing the motion of a rocket is
x = 10 + 5t^2, write an expression for the instantaneous speed of the rocket. What is the instantaneous speed at 5 s. What is the acceleration?

WHere do I begin? Do I need to take the integral anywhere?

2. Sep 25, 2006

### big man

differentiate x = 10 +5t^2 with respect to t to get velocity and then differentiate your new velocity expression with respect to t to get the acceleration.

Given your expression for x your acceleration is going to be a constant.

3. Sep 25, 2006

### needhelp83

Velocity
x=10+5t^2
Derivative with respect to t= 10t
Instantaneous speed of rocket=10t

Instantaneous speed at 5 s
v=10t
v=50 m/s
Would this be in the correct units?

Acceleration
a=10

4. Sep 25, 2006

### big man

yeah those are SI units so they are the correct units. Where the acceleration has units of $$\frac {m} {s^2}$$.

5. Sep 25, 2006

### needhelp83

So if I am understanding this correctly...

The derivative of x=10+5t^2 with respect to t is the velocity
Expression for instaneous speed of rocket
V=10t

Instantaneous speed at 5 s
v=10t
v=10(5)
v=50 m/s

Acceleration is the derivative of velocity (v=10t) with respect to t
a=10
a=10 m/s^2

Look good?

6. Sep 25, 2006

### big man

Yup that looks fine.