Physics Kinematic Formulas

Distance Speed Time Formula
Speed is a measure of how quickly an object moves from one place to another. It is equal to
the distance traveled divided by the time. It is possible to find any of these three values
using the other two. This picture is helpful:
The positions of the words in the triangle show where they need to go in the equations. To
find the speed, distance is over time in the triangle, so speed is distance divided by time. To
find distance, speed is beside time, so distance is speed multiplied by time.
, ,
, ,
s = speed (meters/second)
d = distance traveled (meters)
t = time (seconds)
Distance Speed Time Formula Questions:
1) A dog runs from one side of a park to the other. The park is 80.0 meters across. The dog
takes 16.0 seconds to cross the park. What is the speed of the dog?
Answer: The distance the dog travels and the time it takes are given. The dog’s speed can
be found with the formula:
s = 5.0 m/s
The speed of the dog is 5.0 meters per second.
2) A golf cart is driven at its top speed of 27.0 km/h for 10.0 minutes. In meters, how far
did the golf cart travel?
Answer: The first step to solve this problem is to change the units of the speed and time so
that the answer found will be in meters, since this is what the question asks for. The speed
is:
s = 27.0 km/h
s = 7.50 m/s
Converting the units, the speed is 7.50 m/s. The time the cart traveled for was:
t = 10.0 min
t = 600s
The speed of the cart and the time of travel are given, so the distance traveled can be found
using the formula:
d = st
d = (7.50 m/s)(600 s)
d = 4500 m
The golf cart traveled 4500 m, which is equal to 4.50 km.
Acceleration Formula
Acceleration is a measure of how quickly the velocity of an object changes. So, the
acceleration is the change in the velocity, divided by the time. Acceleration has a magnitude
(a value) and a direction. The direction of the acceleration does not have to be the same as
the direction of the velocity. The units for acceleration are meters per second squared
(m/s2).
a = acceleration (m/s2)
vf = the final velocity (m/s)
vi = the initial velocity (m/s)
t = the time in which the change occurs (s)
Δv = short form for "the change in" velocity (m/s)
Acceleration Formula Questions:
1) A sports car is travelling at a constant velocity v = 5.00 m/s. The driver steps on the gas,
and the car accelerates forward. After 10.0 seconds, the driver stops accelerating and
maintains a constant velocity v = 25.0 m/s. What was the car’s acceleration?
Answer: The initial velocity is vi = 5.00 m/s, in the forward direction. The final velocity
is vf = 25.0 m/s in the forward direction. The time in which this change occurred is 10.0 s.
The acceleration is in the forward direction, with a value:
The car's acceleration is 2.00 m/s2, forward.
2) A child drops a rock off of a cliff. The rock falls for 15.0 s before hitting the ground. The
acceleration due to gravity is g = 9.80 m/s2. What was the velocity of the rock the instant
before it hit the ground?
Answer: The rock was released from rest, so the initial velocity is vi = 0.00 m/s. The time
in which the change occurred is 15.0 s. The acceleration is 9.80 m/s2. The final velocity
must be found, so rearrange the equation:
vf = vi + at
vf = 0.00 m/s +(9.80 m/s2)(15.0 s)
vf = 147 m/s
The rock is falling, so the direction of the velocity is down.
Velocity Formula
Velocity is a measure of how quickly an object moves. So, the velocity is the change in the
position of an object, divided by the time. Velocity has a magnitude (a value) and a
direction. The unit for velocity is meters per second (m/s).
v = velocity (m/s)
xf = the final position (m)
xi = the initial position (m)
t = the time in which the change occurs (s)
Δx = short form for "the change in" position (m)
Velocity Formula Questions:
1) A sail boat is in a 1000 m race, and it crosses the starting line when it is already at full
speed. It reaches the finish line in exactly 1 minute and 20 seconds ( = 80.0 s). What is the
velocity of the sail boat?
Answer: The initial position is the starting line, which we can give the value xi = 0.00 m.
The finish line is 1000 m from the start, so xf = 1000 m. The time it takes the sail boat to
travel that distance is t = 80.0 s. The velocity can be found using the equation:
v = 12.5 m/s
The velocity is 12.5 m/s, in the direction of the finish line.
2) Each floor in a tall building is 3.00 m high. When it's moving, the elevator in this building
moves at a constant velocity of 1.50 m/s. If the first floor is at position 0.00 m, the second
floor is at position 3.00 m, and so on, how much time does it take for the elevator to go
from the sixth (6th) to the eighteenth (18th) floor?
Answer: The initial and final positions of the elevator can be found using the floor numbers
and the distance between floors. The initial floor is 6, so the initial position is:
xi = (6)(3.00 m)
xi = 18.0 m
and the final floor is 18, so the final position is:
xf = (18)(3.00 m)
xf = 54.0 m
The velocity (which we assume to be constant) is v = 1.50 m/s. The time must be found, so
rearrange the equation:
t = 24.0 s
The time it takes for the elevator to travel from the sixth to the eighteenth floor
is 24.0 seconds.

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Distance Speed Time Formula

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