Question

A Honda Civic travels in a straight line along a road. Its distance x from a stop sign is given as a function of time t by the equation x(t)= α t2− β t3, where α = 1.43m/s2 and β = 4.60×10−2m/s3 .
1)Calculate the average velocity of the car for the time interval t=0 to t1 = 2.04s
2)Calculate the average velocity of the car for the time interval t=0 to t2 = 4.09s .
3)Calculate the average velocity of the car for the time interval t1 = 2.04s to t2 = 4.09s .

Answer 1

velocity=d distance/dtime= d/dt (a t^2-Bt^3)
velocity=2A*t -3Bt^2
a) average= (v(2.04)-v(o))/2.04 where
v(2.04)= 2A*2.04-3B*2.04^2 where A, B are given.

Answer 2

A small rock is thrown vertically upward with a speed of 12.0 m/s from the edge of the roof of a 23.0 m tall building. The rock doesn't hit the building on its way back down and lands in the street below. Air resistance can be neglected.
Part A
What is the speed of the rock just before it hits the street?
Express your answer with the appropriate units.