Concept explainers
(a) Use the data in Problem 3 to construct a smooth graph of position versus time. (b) By constructing tangents to the x(t) curve, find the instantaneous velocity of the car at several instants. (c) Plot the instantaneous velocity versus time and, from this information, determine the average acceleration of the car. (d) What was the initial velocity of the car?
(a)
The graph of position versus time.
Answer to Problem 10P
Therefore, the smooth graph of position versus time is shown in Figure I.
Explanation of Solution
The following table contains the data of position of the car at various time instants.
Draw the graph of position versus time for the derby car.
Figure I
In the shown graph, the position of the car at various time instants is plotted in the vertical axis against the time along horizontal direction.
Conclusion:
Therefore, the smooth graph of position versus time is shown in Figure I.
(b)
The instantaneous velocity of the car at various time instants.
Answer to Problem 10P
The instantaneous velocity of the car at
Explanation of Solution
The following table contains the data of position of the car at various time instants.
The instantaneous velocity is the slope of the tangent of the position versus time graph at an instant.
Formula to calculate the slope of the tangent is,
Here,
Draw the tangent line at the time instant of
Figure II
Substitute
Therefore, the instantaneous velocity of the car at
Draw the tangent line at the time instant of
Figure III
Substitute
Therefore, the instantaneous velocity of the car at
Draw the tangent line at the time instant of
Figure IV
Substitute
Therefore, the instantaneous velocity of the car at
Draw the tangent line at the time instant of
Figure V
Substitute
Therefore, the instantaneous velocity of the car at
Draw the tangent line at the time instant of
Figure VI
Substitute
Conclusion:
Therefore, the instantaneous velocity of the car at
(c)
The average acceleration of the car.
Answer to Problem 10P
The average acceleration of the car is
Explanation of Solution
The following table contains the instantaneous velocity of the car at various times instant.
The graph of instantaneous velocity versus time for the derby car is shown below.
Figure VII
The figure VII shows that velocity of the car increases linearly, it means the acceleration of the car is constant throughout the motion.
Thus, the slope of this graph gives the average acceleration of the car.
Formula to calculate the slope of versus time graph is,
Here,
Substitute
From the graph, the slope of the graph is
Conclusion:
Therefore, the average acceleration of the car is
(d)
The initial velocity of the car.
Answer to Problem 10P
The initial velocity of the car is zero.
Explanation of Solution
The equation for the velocity of the car obtained from the graph is,
The first equation of motion gives the velocity of an object at any instant.
Here,
Compare equation (I) and (II).
Thus, the initial velocity of the car is zero.
Conclusion:
Therefore, the initial velocity of the car is zero.
Want to see more full solutions like this?
Chapter 2 Solutions
Physics:f/sci.+engrs.,ap Ed.
Additional Science Textbook Solutions
MODERN PHYSICS (LOOSELEAF)
Lecture- Tutorials for Introductory Astronomy
Physics: Principles with Applications
Essential University Physics (3rd Edition)
College Physics (10th Edition)
The Physics of Everyday Phenomena
- Two mobiles start from the same point of a circumference and have the same initial speed V0, although they leave in opposite directions. One of the movements is accelerated and the other retarded, but the module of its acceleration and deceleration respectively is the same.a) Calculate the value of at, knowing that the mobile endowed with retarded movement at the moment of the meeting has zero speed .b) Find the total acceleration of each of the mobiles at the moment of the encounterarrow_forward(a) What is the magnitude of the average acceleration of a skier who, starting from rest, reaches a speed of 10.8 m/s when going down a slope for 3.36 s? (b) How far does the skier travel in this time?arrow_forwardIf no brakes are used immediately, an automobile with a starting velocity of 30 mph or 44 feet/s will collide with a person. If the driver is inebriated, he or she will be able to respond to the situation in three seconds. If the driver is not intoxicated, he or she can react for about 0.75 seconds. Determine the shortest stopping distance required for the driver (intoxicated, under influence of alcohol) to break on time if the automobile accelerates at -2 feet/s2. a.) 721 ft b.) 517 ft c.) 616 ft d.) 800 ftarrow_forward
- A sailboat starts from rest and accelerates at a rate of 0.12 m/s2 over a distance of 280 m. (a) Find the magnitude of the boat's final velocity. (b) Find the time it takes the boat to travel this distance.arrow_forwardA) Calculate the acceleration over the period from 20 to 60 seconds ? B) The time period during which the object is moving with zero acceleration 0 s to 20 s Or 20 s to 60 s ?arrow_forwardProfessional Application: Blood is accelerated from rest to 30.0 cm/s in a distance of 1.80 cm by the left ventricle of the heart. (a) Make a sketch of the situation. (b) List the knowns in this problem. (c) How long does the acceleration take? To solve this part, first identify the unknown, and then discuss how you chose the appropriate equation to solve for it. After choosing the equation, show your steps in solving for the unknown, checking your units. (d) Is the answer reasonable when compared with the time for aheartbeat?arrow_forward
- A running race has a total distance d. The winner runs at a steady speed of v0 and the second placefinisher runs at a speed that is 4/5 of the winner’s speed. (a) How much time passes between each runnerfinishing? (b) The winner didn’t realize they pass the finish line. What is the total distance the winnerhas ran when the second place finisher finishes? (c) Sketch a single position plot with curves for bothrunners on it. Draw a horizontal line to represent the finish.Now suppose a swimmer swims the length of a pool, with length L, in some time t0. They then swim thereturn trip in time3/5t0. (d) What is the average velocity in the first half of the swim, the second half ofthe swim, and for the total swim? (e) Same as previous part, but answer for average speed instead.arrow_forwardA typical sneeze expels material at a maximum speed of 55.4 m/s. Suppose the material begins inside the nose at rest, 2.00 cm from the nostrils. It has a constant acceleration for the first 0.250 cm and then moves at constant velocity for the remainder of the distance. A) What is the acceleration as the material moves the first 0.250 cm? B) How long does it take to move the 2.00-cm distance in the nose? C) Which of the following is the correct graph of vx(t) if the sneeze expels material at a maximum speed of 44.0 m/s and has a constant acceleration for the first 0.250 cm and then moves at constant velocity for the remainder of the distance?arrow_forwardproblem is incorrect. Good luck. A ball has an initial velocity of 1.50 m/s along the x-axis. Starting at t,-0, the ball receives an acceleration of 2.8 m/s in the y-direction. Find the following: a) What is the position and distance from the starting point of the ball 3.0 seconds after ,? b) What is the velocity in both magnitude and direction of the ball at 3.0 seconds? c) Provide a plot of position vs time from ,=0 to t=3.0seconds. GEP 30arrow_forward
- (a) Sketch a graph of acceleration versus time corresponding to the graph of velocity versus time given in the following figure. (b) Identify the time or times (ta, tb, tc, etc.) at which the acceleration has the greatest positive value. (c) At which times is it zero? (d) At which times is it negative?arrow_forwardAs a technical engineer in the army, you are part of a team in charge of testing and commissioning a new tank recently purchased by the artillery Field testing has revealed the following information: 1) The tank moves from rest to a speed of 70 ??/ℎ? in 10 seconds. 2) Using the breaking system, the tank is brought to a complete stop from a speed of 70 ??/ℎ? in 5 seconds a) Find the average driving acceleration of the tank. b) Calculate the average breaking acceleration of the tank. c) For parts (a) and b above parts report your answers in US Customary Units (mile/hr) so that the information could be shared with experts from the US.arrow_forwardAn object traveling on a horizontal surface with an initial velocity of 12.0 m/s to the right is then accelerated 3.00 m/s2 towards the left. (a) Calculate the magnitude of this object's displacement at values of time: 0.00, 4.00, and 8.00 s. (b) Calculate the speed for the same times. (c) Describe the motion of the object for this time interval.arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning