Question

A turtle crawls along a straight line, which we will call the 𝑥-axis with a positive direction to the right. The equation for the turtle’s position as a function of time is 𝑥(𝑡) = 50.0𝑐𝑚 + (12.00𝑐𝑚/𝑠 2 )𝑡. (a) Find the turtle’s initial velocity, initial position, and initial acceleration. (b) At what time 𝑡 is the velocity of the turtle zero?

Answer 1

Given:

$x(t)=50.0+12.00t^2\:\rm (cm)$

The turtle’s velocity

$$v(t)=x'(t)=24.00t\:\rm cm/s$$

The turtle’s acceleration

$$a(t)=v'(t)=24.00\:\rm cm/s^2$$

(a) The turtle’s

initial velocity:

$$v(0)=0\:\rm cm/s$$

 initial position:

$$x(0)=50.0+12.00*0^2=50\:\rm cm$$

initial acceleration:

$$a(0)=24.00\:\rm cm/s^2$$

(b) The velocity of the turtle is zero at the instant

$$t=0\:\rm s$$