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

The equation of motion of the turtle is given by

$$𝑥(𝑡) = 50.0\:{\rm cm} + (12.00{\:\rm cm/s^2} )𝑡^2.$$

(a) the turtle’s initial position

$$x_0=x(0)=50.0\:\rm cm$$

the turtle’s velocity

$$v(t)=x'(t)=24.0{\:\rm cm/s^2}t$$

the turtle’s initial velocity

$$v_0=v(0)=0$$

the turtle’s initial acceleration

$$a(0)=v'(0)=24.0\:\rm cm/s^2$$

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

$$t=0$$