The position of the front bumper of a test car under microprocessor control is g

Question

The position of the front bumper of a test car under microprocessor control is given by x(t) = 217 m + (480s ):2 the car has zero velocity. 4. (0.100,t6 Find its position and acceleration at the instants when 5. A small block has constant acceleration as it slides down a frictionless incline. The block is released from rest at the top of the ineline, and its speed after it has traveled 6.80 m to the bottom of the incline is 3.80 m/s. What is the speed of the block when it is 3.40 m from the top of the incline? A small rock is thrown vertically upward with a speed of 22.0 m/s from the edge of the roof of a 30.0- m-tall building. The rock doesn't hit the building on its way back down and lands on the street below Ignore air resistance. 6. What is the speed of the rock just before it hits the street? How much time elapses from when the rock is thrown until it hits the street? a.

Explanation / Answer

4.

x = 2.17 + 4.8 t^2 - 0.1 t^6

v = dx/dt = 9.6 t - 0.6 t^5 = 0

t( 9.6 - 0.6 t^4) = 0

t = 0 or 2 sec

so velocity is zero at t = 2sec.

and a = dv/dt = 9.6 - 3 t^4 = 0

putting t = 2 sec

a = -38.4 m/s^2

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