Motion Along a Straight Line

Question 1

Derive the two equations that make most equations for for a particle traveling with constant acceleration in a line.

Answer 1

dv/dt = a

⇒ v - v_o = at

dx/dt - v_o = at

⇒ x - x_o = v_ot + ½at²

Question 2

A bolt is dropped from a bridge under construction, falling 90 m to the valley below the bridge. (a) In how much time does it pass through the last 20% of its fall? What is its speed (b) when it begins that last 20% of its fall and (c) when it reaches the valley beneath the bridge?

Answer 2

(a) -90 m = -½gt²_total, -18 m = -½gt²_{last 20%}, T = t_total - t_{last 20%}
(b) v = -aT
(c) v = -at_total

Question 3

A rock is dropped (from rest) from the top of a 60-m-tall building. How far above the ground is the rock 1.2s before it reaches the ground?

Answer 3

-60 m = -½at²_total

T = t_total - 1.2s

Δy = -½aT²

60 - Δy = how far above the ground.

Question 4

A ball is thrown vertically downward from the top of a 36.6-m-tall building. The ball passes the top of a window that is 12.2 m above the ground 2.00 s after being thrown. What is the speed of the ball as it passes the top of the window?

Answer 4

(36.6 - 12.2) m = v(2.00 s) - ½a(2.00 s)²

Question 5

A parachutist bails out and freely falls 50 m. Then the parachute opens, and thereafter she decelerates at 2.0 m/s². She reaches the ground with a speed of 3.0 m/s. (a) How long is the parachutist in the air? (b) At what height does the fall begin?

Answer 5

-50 = -½•a•t²_{no par.}

right before opening the parachute v² = 2•a•50

So, 3.0 m/s = (2•a•50)^½ - at_par.

Δy = v²t_par - ½at²_par

50 + Δy = height at which the fall began.