RMIT University
OENG1209 – Engineering Sciences – Homework 2
Kinematics
Question 1: Instantaneous Velocity
A man leaves his house and walks along the sidewalk toward a bus stop. After 5 minutes, it
starts to rain and he returns home. His distance from his house as a function of time is shown
below. At which of the labeled point is his velocity:
a) Zero?
b) Constant and Positive?
c) Constant and Negative?
d) Increasing in magnitude?
e) Decreasing in magnitude?
Justify your answer.
Answer: a) point IV, b) point I, c) point V, d) point II, e) point III
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RMIT University
OENG1209 – Engineering Sciences – Homework 2
Kinematics
Question 2: Average vs Instantaneous Velocity
The position of a rabbit along a straight tunnel as a function of time is plotted in the graph
below. Determine:
a) The instantaneous velocity of the rabbit at t = 10 secs and t = 30 sec.
b) The average velocity of the rabbit between 0 and 5 secs.
c) The average velocity of the rabbit between 25 and 30 secs.
d) The average velocity of the rabbit between 40 and 50 secs.
Answer: a) V @ 10 secs = 0.3 m/s forward, V @ 30 secs = 1.2 m/s forward, b) Average V
between 0 and 5 secs is 0.30 m/s forward, c) Average V between 25 and 30 secs is 1.4 m/s
forward, d) Average V between 40 and 50 secs is -0.95 m/s backward.
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RMIT University
OENG1209 – Engineering Sciences – Homework 2
Kinematics
Question 3: Kinematic Equations
In the fastest measured tennis serve, the ball left the racquet at 73.14 m/s. A served tennis ball
is typically in contact with the racquet for 30.0 milliseconds and starts from rest. Assume the
ball was accelerated at a constant rate.
a) What was the ball’s acceleration during this serve?
b) How far did the ball travel during the serve?
Answer: a) 2440 m/s^2, b) 1.10 meters
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RMIT University
OENG1209 – Engineering Sciences – Homework 2
Kinematics
Question 4: Kinematic equations
Mary and Sally are in a foot race. When Mary is 22 m from the finish line, she as a speed of
4.0 m/s and is 5.0 m behind Sally, who has a speed of 5.0 m/s. Sally thinks she as an easy win
and so, during the remaining portion of the race, decelerates at a constant rate of 0.40 m/s2 to
the finish line. What constant acceleration does Mary now need during the remaining portion
of the race, if she wishes to cross the finish line side-by-side with Sally?
Answer: About 0.70 m/s^2
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RMIT University
OENG1209 – Engineering Sciences – Homework 2
Kinematics
Question 5: Projectile Motion
A fire hose held near the ground shoots water at a speed of 6.5 m/s. At what angle(s) should
the nozzle point in order that the water land 2.5 meters away? Sketch the trajectories of the
water stream and indicate the initial velocity vector(s) of the stream.
Answer: There are 2 angles, around 18o and 72o. In both cases, you will have a parabola, but
each parabola will have a different peak.
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RMIT University
OENG1209 – Engineering Sciences – Homework 2
Kinematics
Question 6: Inclined motion
On mountainous downhill roads, escape routes are sometimes placed to the side of the road for
trucks whose brakes might fail. Assuming the escape route has a constant upward slope of 26𝑜 ,
calculate the horizontal and vertical components of the acceleration of a truck that slowed from
110 km/hr to rest in 7.0 seconds.
Answer: 𝑎⃗ = [−3.9, −1.9] 𝑚/𝑠 2
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RMIT University
OENG1209 – Engineering Sciences – Homework 2
Kinematics
Question 7: Relative Motion
A boat, whose speed in still water is 2.50 m/s, must cross a 285 meters wide river and arrive at
a point 118 meters upstream from where it starts as illustrated below. To do so, the pilot must
head the boat at a 45.0o upstream angle. What is the speed of the river’s current?
Answer: The river is flowing at about 1.0 m/s to the left of the picture.
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