How Do You Solve for Velocity and Position in Calculus Problems?

[black_hole]

Homework Statement

a9t) = 1.2t. If v(1) = 5m/s, v(2) = ?
If x(1) = 6m, x(2) = ?

Homework Equations

The Attempt at a Solution

I know (anti-deriv) that is something like v(t) = .6t^2, but plug in 1 and that's not 5m/s?

 

[collinsmark]

Homework Statement

a9t) = 1.2t. If v(1) = 5m/s, v(2) = ?
If x(1) = 6m, x(2) = ?

Homework Equations

The Attempt at a Solution

I know (anti-deriv) that is something like v(t) = .6t^2, but plug in 1 and that's not 5m/s?

It took me the longest time to figure out what you meant by "a9t) = 1.2t"

Do you mean, a(t) = (1.2 [m/s³])t
?

When evaluating indefinite integrals (i.e. anti-derivatives), ensure you add an arbitrary constant to the results.

In other words, for this problem,

v(t) = (0.6 [m/s³])t² + v₀

where v₀ is an arbitrary constant. Use v(1 ) = 5 [m/s] to solve for v₀.

'Same idea applies when solving for x(t).