AP Calc Q: Find Time When Object at x=10/3

[ERAUin08]

Hey guys I need some help with one of my AP Calc question. My luck is that it will be very simple. Thanks for your help

Homework Statement

The velocity of an object, starting at the origin, and moving along the x-axis is given by
V(t)=(t-1)(t+1)^1/2. Find the time when the object will be at x=10/3. Units are not given. Since we are dealing with the x-axis I am using units as the measurement of distance and second as the measurement as time.

The Attempt at a Solution

My attempt to find t was to set 10/3 equal to my V(t) which I then got 13.842 seconds. Then to see if this is possibly a reasonable answer I substituted 13.842 in for t and found the velocity which was 3.593 units per second.

Im not really sure if I am approaching this problem correctly. I feel that what I did was a little too easy for second semester calculus. Thanks for your help everyone.

 

[G01]

V(t) is a velocity function, not a position function. You cannot set the position x=10/3 equal to the velocity function, V(t).

HINT: You need to use your velocity function, V(t), to find a position function, x(t).