Finding position from velocity

[bobsmith76]

Homework Statement

Give the velocity v = ds/dt and initial position of a body moving along a coordinate line.
Find the body's position at time t.

v = 32t - 2, s(.5) = 4

The Attempt at a Solution

Here's how the solution manual does it:

step 1. v = ds/dt = 32T - 2

step 2. s = 16T^2 - 2T + C; at s = 4 and T = .5 (I understand this)

step 3. (find C)

C = 1 (I understand how to do that)

step 4. therefore

s = 6T^2 - 2T + 1

Why 6T^2? How did they get that. I don't understand.

 

[tylerc1991]

...
step 4. therefore

s = 6T^2 - 2T + 1

Why 6T^2? How did they get that. I don't understand.

That looks like a typo on their part. The answer is 16t^2 - 2t + 1, as you originally got.