Physics help?

Question

A turtle crawls along a straight line, which we 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)= 50.0 cm + (2.00 cm/s)t- (0.0625 cm/s squared)t squared.
a) Find the turtle's initial velocity, initial position and initial acceleration.
b) At what time t is the velocity of the turtle zero.

Thanks.

Answer 1

Ok, we have the position as a function of time :

x(t) = 50.0 cm + (2.00 cm/s)t- (0.0625 cm/s squared)t squared.

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

you know that the first derivative of position respect of time is the velocity as a function of time :

dX / dt = v(t)

v(t) = 2 - 0.125t

The initial velocity is when t = 0s

v(t) = 2 - 0.125*0 = 2 m/s >>> initial velocity

b) v(t) = 2 -0.125t

v(t) = 0, when ?

2 - 0.125t = 0 >>> t = 16s

Hope that helped you