1. The document discusses instantaneous velocity and equations of motion for objects in rectilinear motion. It provides examples of calculating instantaneous velocity from equations of motion for balls being thrown upward and falling objects. 2. Questions are given about finding instantaneous velocities at certain times, the time for an object to reach its highest or lowest point, and the maximum or minimum height, based on equations of motion provided. 3. The final problem asks to find the instantaneous velocity at given times based on three equations of motion.

1. 1. RATE PROBLEMS: INSTANTANEOUS VELOCITY
(PHYSICS)
RECTILINEAR MOTION
𝑠 = 𝑓(𝑡) (EQUATION OF MOTION)
WHERE S = DIRECTED DISTANCE FROM POINT
O TO THE
PARTICLE AT A PARTICULAR INSTANT
OF TIME.
T = TIME
𝑓(𝑡) = THE DISTANCE, WHICH IS THE
FUNCTION OF TIME

2. If 𝒇 is a function given by the equation:
𝒔 = 𝒇(𝒕)
(𝒔 is the number of units in the directed distance of the
particle from a fixed point on the line at 𝒕 units of time)
Then, the instantaneous velocity of the particle at 𝒕 units of
time is 𝒗 units of velocity, where
𝒗 = 𝒇′
𝒕 ⟺ 𝒗 =
𝒅𝒔
𝒅𝒕

3. The ball is thrown vertically upward from the ground with an initial velocity of
64 𝑓𝑡./𝑠𝑒𝑐. If the positive direction of the distance from the starting point is
up, the equation of motion is 𝑠 = − 16𝑡2 + 64𝑡.
If 𝑡 is the number of seconds in the time that has elapsed since the ball
was thrown and 𝑠 is the number of feet in the distance of the ball from the
starting point at 𝑡 s ec.
a. Find the instantaneous velocity of the ball at the end of 1 sec. Is the
ball rising or falling at the end of 1 sec?
b. Find the instantaneous velocity of the ball the the end of 3 sec. Is the
ball rising or falling at the end of 3 sec?
c. How many seconds does it take for the ball to reach its highest point?
d. How high will the ball go?
e. How many seconds does it take for the ball to reach the ground?


4. It has been found by experiment that a body falling from rest under
the influence of gravity, follows approximately this equation of
motion:
s = -2t2 + 5t + 3; where s is the distance fallen measured in
meters; t is the time elapsed measured in seconds.
 Find the instantaneous velocity at the end of 2 seconds.
 At what time does an object reach its maximum height?
 What is the maximum height of an object?
 How long before an object reach the ground?

5. A body moves in a straight line according to this equation of
motion:
s = -3t2 + 27t; where t is measured in seconds and s in meters.
 What is the instantaneous velocity of an object at the end of 2
seconds?
 How long does it take before an object reach its maximum
height?
 What is the maximum height of an object?
 How long before an object reach the ground?

6. Determine the maximum or minimum height of an object given the
following equation of motion:
1. S = -12t2 + 24t; find v(t) = 3sec
2. S = 7t2 -42t ; find v(t) = 5 sec
3. S = 25t2 – 150t ; find v(t) = 4sec.