PHY 2053, Spring 2009, Quiz 2 — Whiting
1. A vehicle accelerates uniformly from rest to 60 m/s in 12 seconds. Find:
a) the distance the vehicle travels during that time,
Use x = (v + v0 ) × t/2 to solve for x:
x=
(60 + 0)
× 12 = 360 m.
2
b) the constant acceleration of the vehicle.
Use = (v + v0 ) × t/2 to solve for x: and solve for a:
a=
(60 − 0)
(v − v0 )
=
= 5 m/s2 .
t
12
Check that these make sense:
v 2 = v02 + 2a × x ⇒ 602 = 02 + 2 × 5 × 360 = 3600.
This is correct, so we are looking good.
2. A bullet is fired straight through a board 5-cm thick, entering with a speed of 200 m/s
and emerging with a speed of 100 m/s. Find:
a) the acceleration of the bullet as it passes through the board,
Use v 2 = v02 + 2a × x and solve for a:
(v 2 − v02 )
(1002 − 2002 )
a=
=
= −300, 000 m/s2 .
2×x
2 × 0.05
b) the total time the bullet is in contact with the board?
Use x = (v + v0 ) × t/2 to solve for t:
t=
2×x
2 × 0.05
=
= 0.33 ms.
(v + v0 )
(100 + 200)
Let’s check this by substituting in v = v0 + a × t:
100 = 200 − 300, 000 ×
1
× 10−3 = 100
3
so both our answers make sense — they are consistent with each other.