A Turtle crawls along a straight line, which we will call the x - axis, with the

Question

A Turtle crawls along a straight line, which we will call the x - axis, with the positive direction to the right. The equation for the turtle's position as a function of time is x(t) = 65. 0cm + (1. 50 cm/s)t - (0. 0650 cm/s^2)t^2 a) Find the turle's initial velocity, initial position, and acceleration. X(t) = c_0 + v_0 t + 1/2 a t^2 x_0 = 65.0 cm n_0 = 1.50 cm/3 a = sigma (0.0660 cm/s^2) = 0.13 cm/s^2 = 0.0013 m /s^2 b) At what time t is the velocity of the turtle v(t) = 0 m/s? v(t) = v_0 + a t v(t) = 65.0 cm + 0.13 cm/s^2

Explanation / Answer

We know :
x = 65cm + 1.5cm/s*t - 0.065cm/s^2*t^2

v = d(x)/dt
Hence,
v = 0 + (1.5cm/s) - (2*0.065cm/s^2)*t
v(t) = (1.5cm/s) - (0.130 cm/s^2)*t

a = d(v)/dt
a = 0 - (0.130 cm/s^2)
a = -0.13 cm/s^2

a)
Initial Velocity
v(t) = (1.5cm/s) - (0.130 cm/s^2)*t
v(0) = (1.5cm/s) - (0.130 cm/s^2)*0
v(0) = 1.5 cm/s

Initial Position
x(0) = 65cm + 1.5cm/s*t - 0.065cm/s^2*t^2
x(0) = 65cm + 1.5cm/s*0 - 0.065cm/s^2*0^2
x(0) = 65 cm

acceleration :
a = -0.13 cm/s^2

b)
v(t) = 0 cm/s

0 = (1.5cm/s) - (0.130 cm/s^2)*t
(0.130 cm/s^2)*t = 1.5
t = 1.5/0.13 = 11.54 s

c)
x(t) = 0
x(t) = 65cm + 1.5cm/s*t - 0.065cm/s^2*t^2
65cm + 1.5cm/s*t - 0.065cm/s^2*t^2 = 0
t = = 45.2005 sec

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