PHYS 125: Motion in one Dimension
HM #2
University of Science and Technology Zewail City
Fall 2025
1. A car moves rectilinearly, it first accelerates from rest with an
acceleration of 𝑎 = 5.0 𝑚/𝑠 2 , then with no acceleration, and finally,
decelerating at the same rate 𝑎 until it stops. The total duration of the
motion is 𝑡 = 25 𝑠 , and the car’s average velocity during this time is
𝑣𝑎𝑣𝑔 = 72 𝑘𝑚 /ℎ𝑟 .
How long does the car move with no acceleration?
2. A ball is dropped from rest at height 4h. After it has fallen a distance d,
a second ball is dropped from rest at height h. What should d be (in
terms of h) so that the balls hit the ground at the same time?
3. A particle moves in the positive direction of the x axis starting from
the origin with initial velocity with a magnitude 𝑣0 = 10.0 𝑐𝑚/𝑠 . Its
velocity, after that, can be described by:
𝑡
𝑣 = 𝑣0 (1 − )
𝛼
a. where 𝛼 is a constant 𝛼 = 5.0 𝑠.
Find its position after 6 seconds. Do the same at 10 s and 20 s.
b. What are the times when the distance of the particle is 10 cm after
the start of the motion.
c. The particle covers a distance s after t seconds from the start of the
motion. Find 𝑠(4) and 𝑠(8). Draw the approximate plot s (t).
4. An elevator starts moving upward from the ground with a constant
speed 𝑣0 . At a later time 𝑇1 , a boy inside the elevator drops a tiny ball
through a hole in the floor. The ball then falls freely and reaches the
ground after 𝑇2 seconds. Find the height of the elevator at the instant
the ball is dropped.
5. Jerk is defined as the rate of change of acceleration. Consider a
particle moving in one dimension with constant jerk j. Determine the
position x(t) of the particle in terms j and the initial values 𝑥0 , 𝑣0 , and
𝑎0 .