NASA-Threads
Work and Mechanics
Lesson 7: 1D Particle Motion
Effect of Initial Velocity
We have been solving problems where objects are dropped from rest (they were not
moving until we let them go).Let’s look at situations where a body is moving upward or
downward at t=0. That is, let’s solve problems where an object has an initial velocity.
Assume a body is traveling upward with an initial velocity of vo and is acted on by gravity
which accelerates the body downward at g (9.81 m/s2 on earth). The body will slow down,
reach a peak height, and then start back down. The velocity at any time t is . . .
𝑣 = 𝑣𝑜 + 𝑎 ∙ 𝑡
= 𝑣𝑜 + (−𝑔) ∙ 𝑡
Initial velocity
Decrease in the velocity due to gravity
(the body is accelerating downward at a
rate of 9.81 m/s2)
downward velocity = negative
upward velocity = positive
CLASS PROBLEM: An object bounces off the floor (on earth) and moves upward
with an initial velocity of 5 m/s. Neglecting the influence of drag, determine the
time required for the body to bounce to its peak height. HINT: What is the
velocity of the ball at its peak height?
NASA-Threads
Work and Mechanics
Lesson 7: 1D Particle Motion
Effect of Initial Position
Assume that the object starts moving upward at a height of yo with a velocity of vo. How
does the position y vary with time?
height = initial height + vavg ∙ time
y=ymax
𝑦 = 𝑦𝑜 + 𝑣𝑎𝑣𝑔 ∙ 𝑡
y
y=yo
y=0
= 𝑦𝑜 +
𝑣 + 𝑣𝑜
∙𝑡
2
𝑣𝑜 + 𝑎 ∙ 𝑡 + 𝑣𝑜
= 𝑦𝑜 +
∙𝑡
2
𝑎 ∙ 𝑡2
𝑦 = 𝑦𝑜 + 𝑣𝑜 ∙ 𝑡 +
2
CLASS PROBLEM: An object bounces off the floor (on earth) and moves upward
with an initial velocity of 5 m/s. Neglecting the influence of drag, determine the
bounce height of the object. HINT: Use the time of flight from the previous
problem.
NASA-Threads
Work and Mechanics
Lesson 7: 1D Particle Motion
NASA-Threads
Work and Mechanics
Lesson 7: 1D Particle Motion
CLASS PROBLEM: A probe moves vertically downward toward the moon at an
elevation of 2000 m and a velocity of 100 m/s. Assume that the change in velocity
of the probe is influenced only by the gravitational pull of the moon? Remember
that the moon has no atmosphere (no drag) and that the gravitational
acceleration on the moon is 0.165∙g.
(a) Estimate the time required for the probe to reach the surface of the moon.
(b) Estimate the impact velocity of the probe.