# 10-11 problem set3 solutions

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```					Physics Problem Set 3

Problem Set 3 – Velocity Time Graphs and Kinematics

Resources: Course Materials – Motion in a Straight Line. Handout – velocity
time practice. Hewitt Conceptual Physics Chapter 2.

Problem #1 Interpreting Velocity Time Graphs (Proficient)

Velocity vs. Time

30
25
20
Velocity in m/s

15
10
5
0
-5 0           5           10          15           20          25
-10
-15
-20
Time in seconds

a. During which time intervals is the object accelerating? What is the
acceleration? During which time intervals is the object moving with a
constant velocity, and what is this velocity?

The object accelerates at 5 m/s/s from t=4 to t=8 seconds
The object accelerates at -10 m/s/s from t=11 to t=15 seconds

The object moves at a constant velocity of 5 m/s from t=0 to t=4
seconds
The object moves at a constant velocity of 25 m/s from t=8 to t=11
seconds

Useful Information:
1 mile = 1610 m. 1 second = 1000 milliseconds. 1 hour = 3600 seconds.
Physics Problem Set 3

The object moves at a constant velocity of -15 m/s from t=15 to t=20
s.

b. Is the object ever at rest in these 10 seconds (is the velocity ever
zero)?

It is not at rest in the first 10 seconds. The object’s velocity is 0 m/s
at t=13.5 seconds.

c. What is the displacement of the object in the first 4 seconds?

(5 m/s)(4 s) = 20 meters

d. What is the total displacement of the object from 0 to 15 seconds
(don’t forget, displacement can be negative)?

The displacement ∆x in the first 15 seconds is 175 meters.

e. Describe the motion of the object at time = 13.5 seconds?

The velocity is zero, and the moving object is changing direction.

f. What is the total displacement of the object from 0 to 20 seconds?

The displacement ∆x over 20 seconds is 100 meters.

g. When does the object have the greatest velocity? What is this
velocity? The greatest acceleration? What is this acceleration?

The greatest velocity is 25 m/s from t=8 to t=11 seconds. The
greatest acceleration is -10 m/s/s from t=11 to t=15 seconds.

Problem #2 - The Speed of Sound vs. The Speed of Light (Proficient)
Sound travels at approximately 340 m/s in air. At this rate, how many
seconds will it take the sound of a thunder clap to reach your ears if the
lightening strike is 1 mile away?

∆t = 4.74 seconds

Useful Information:
1 mile = 1610 m. 1 second = 1000 milliseconds. 1 hour = 3600 seconds.
Physics Problem Set 3

Light travels at approximately 3 x 108 m/s in air. At this rate, how many
seconds will it take the light from a lightning strike to reach your eyes if the
strike is 1 mile away?

∆t = 5.37 x 10-6 seconds

Problem #3 - Road Trip (Proficient)
You set out to drive to Philadelphia during rush hour, and it takes you an
hour to drive 30 km. Your return trip takes only 30 minutes. What was your
average speed for the round trip? What was your average velocity?

SPEEDavg = 0.67 km/min = 1.12 m/sec

Vavg = 0 m/s

Problem #4 – Stop Sign (Proficient)
A car approaches an intersection traveling at 12 m/s. If it takes 3 seconds
to safely stop the car before the stop sign, how far away from the
intersection should the driver start to brake?

∆x = 18 meters

Problem #5 - Bicycle Ride (Proficient)
If a bicycle rider travels at a constant speed of 5 m/s for 30 seconds, and
then accelerates at a rate of 1 m/s/s for 10 seconds, how far will the bicycle
have traveled in this 40 second time interval?

∆x = 250 meters

Problem #6 Battle of the Roller Coasters (Advanced).
The velocity vs. time graphs shown below describe two popular roller
coasters. Determine the maximum velocity of each ride and the length of
the track for each ride. Which do you think would be more fun to ride?

Useful Information:
1 mile = 1610 m. 1 second = 1000 milliseconds. 1 hour = 3600 seconds.
Physics Problem Set 3

Both coasters have a maximum velocity of 50 m/s. The Scream Factory
is 750 m and Ultraman’s Revenge is 635 m long.

A ranger in a national park is driving at 56 km/hr when a deer jumps out onto
the road 65 m ahead of the vehicle. After a reaction time of t seconds, the
ranger applies the brakes to produce an acceleration of -3.0 m/s2. What is

Useful Information:
1 mile = 1610 m. 1 second = 1000 milliseconds. 1 hour = 3600 seconds.
Physics Problem Set 3

the maximum reaction time allowed if the ranger is to avoid hitting the
deer?

The maximum reaction time is 1.58 seconds. Hint – first find the
distance required to stop the car with the given initial velocity and
acceleration.

An object has a constant acceleration of 4 m/s/s. Its velocity is 1 m/s at
t=0, when it is at x=7 m. How fast is it moving when it is at x=8 m?

Vfinal = 3.0 m/s Hint: Use quadratic formula, or look for an expression
relating initial velocity, final velocity, acceleration and displacement
(without time).

Still Want More? Just for Fun!

#9 The Bikes and The Bee
Two bikes travel at a uniform speed
of 10 mph toward each other. At
the moment when they are 20 miles
apart, a bumble bee flies from the
front wheel of one of the bikes at a
uniform speed of 25 mph directly to
the wheel of the other bike. It touches it and turns around in a negligibly
short time and returns at the same speed to the first bike, whereupon it
touches the wheel and instantaneously turns around and repeats the back
and forth trip over and over again – successive trips becoming shorter and
shorter until the bikes collide and squash the unfortunate bee between the
front wheels. What was the total mileage of the bee in its many back and
forth trips from the time the bikes were 20 miles apart until its hapless
end?

25 miles Hint: No math required! 

Useful Information:
1 mile = 1610 m. 1 second = 1000 milliseconds. 1 hour = 3600 seconds.

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