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

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) = 50.0cm+(2.00cm/s)M0.0625cm/s2)t2. Find the turtle's initial velocity. Find the turtle's initial position. Find the turtle's initial acceleration. At what time t is the velocity of the turtle zero? How long after starting does it take the turtle to return to its starting point? A large boulder is ejected vertically upward from a volcano with an initial speed of 40.9m/s. Air resistance may be ignored. At what time after being ejected is the boulder moving at a speed 20.7m/s upward? At what time is it moving at a speed 20.7 m/s downward? When is the displacement of the boulder from its initial position zero? When is the velocity of the boulder zero?

Explanation / Answer

x(t) = 50 + 2t - 0.0625t^2 ......(1)

On derivating the above equation with respect to time, we get

v(t) = 2 - 0.125t ......(2)

(a) For initial velocity, v(0) = 2 cm/sec

(b) Initial position at t=0 sec is x(0) = 50 + 0 - 0 = 50 cm

(c) On differentiating equation (2) with respect to time,

a(t) = -0.125

For initial accleration, a(0) = -.125 cm/sec^2

(d) From equation (2) v(t) = 2 - 0.125t , this will be zero at v(t) = 2 - 0.125t =0

=> t = 2/0.125 = 16 seconds

(e) When is the displacements zero can be obtained by equating equation (1) with 0.

=> x(t) = 50 + 2t - 0.0625t^2 = 0

=> t = 16 + 4sqrt(66) = 48.49 seconds

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