Question

 A deer is moving with its position varying as a function of time according to the equation: x = 18 + 1.75t – 0.04t 2 Where x is in cm and t is in seconds.

i. What is the deer’s: - initial position? - initial velocity? - initial acceleration?

ii. Determine the time when the deer’s velocity is zero?

iii. How long after starting does the deer’s displacement become zero? Where is the deer then?

Answer 1

i. $x_0=18\ (cm)$ ; $v_0=x'(0)=1.75-0.08\cdot0=1.75\ (cm/c)$

$a_0=v'(0)=-0.08\ (cm/c^2)$

ii. $v=1.75-0.08t\to 0=1.75-0.08t\to t=21.875\ (s)$

iii. $\Delta x=0$ if $x=18\ (cm)$ . So,

$18=18+1.75t-0.04t^2\to t=43.75\ (s)$

The deer is at the point $x = 18\ (cm)$ .