Concept explainers
(a)
To find: The magnitude of displacement in meters for the shaded box.
(a)
Answer to Problem 104P
The magnitude of displacement for the shaded region is
Explanation of Solution
Given:
The initial velocity on the box is
The final velocity on the box is
The time interval covered in one box is
Formula used:
The area of the velocity-time graph gives the displacement of the body.
Write the expression for the area of the shaded region.
Here,
Calculation:
Substitute
Conclusion:
Thus, the magnitude of displacement for the shaded region is
(b)
To find:The displacement between the two given time intervals of
(b)
Answer to Problem 104P
The displacement of the particle for the given
Explanation of Solution
Given:
The first
The second
Formula used:
The area of one block of the graph is
Write the expression for the displacement.
Here,
Calculation:
Substitute
Here,
Substitute
Here,
Conclusion:
Thus, the displacement of the particle for the given
(c)
To find:The average velocity of the particle for given time interval.
(c)
Answer to Problem 104P
The average velocity of the particle for the given time period is
Explanation of Solution
Given:
The distance covered in the first interval is
The distance covered in the second interval is
Formula used:
The area of one block of the graph is
The average velocity is defined as the total displacement in the given time period.
Write expression for total displacement of the particle.
…... (3)
Here,
Write the expression for the average velocity of the particle.
Here,
Calculation:
Substitute
Substitute
Conclusion:
Thus, the average velocity of the particle for the given time period is
(d)
To explain: The average displacement of the particle for the given time period and compare it with the answer of part (b) and to compare the average velocity to the mean of initial and final velocity of the particle.
(d)
Answer to Problem 104P
The displacement of the particle for the interval
Explanation of Solution
Given:
The equation of curve is
The time interval is
Formula used:
Write the expression for the velocity of particle.
Rearrange the above expression for
Integrate the above expression from
Write an expression for the mean of initial and final velocity.
Calculation:
Substitute
Substitute
Conclusion:
Thus, the displacement of the particle for the interval
Want to see more full solutions like this?
Chapter 2 Solutions
Physics for Scientists and Engineers
- A person who walks for exercise produces the position-time graph shown. Calculate the average velocity, including sign, for (a) segment A, (b) segment B, (c) segment C, and (d) segment D. +1.25 (a) Number i (b) Number i (c) Number i (d) Number i Position x (km) +1.00 +0.75 +0.50 +0.25 Units Units Units Units A B > C 0.20 0.40 0.60 0.80 1.00 Time (h) < Darrow_forwardThe displacement of a particle is given by s = 3t3 - 53t2 + 115t - 62 where s is in feet and t is in seconds. Plot the displacement, velocity, and acceleration as functions of time for the first 14 seconds of motion. After you have made the plots, answer the questions.Questions: At t = 3 sec, s = ft, v = ft/sec, a = ft/sec2 At t = 7.7 sec, s = ft, v = ft/sec, a = ft/sec2 At t = 11.5 sec, s = ft, v = ft/sec, a = ft/sec2 The velocity is zero when t = sec and when t = secarrow_forwardThe velocity of an object is given by, = u + at V ds dt. where, u is the initial velocity, a is the acceleration, and ₺ is the time in seconds. Solve the differential equation to obtain the displacement, s, given that at t = 0, s = 7 (metres) : 1 if u = 3 ms ¹, a = 2.4 ms 2, calculate the displacements at t = 4.9 seconds. Give your answer to 2 decimal places.arrow_forward
- Speedometer readings for a vehicle (in motion) at 13-second intervals are given in the table. t (sec) v (ft/s) 28 13 21 26 24 39 19 52 26 65 18 Estimate the distance traveled by the vehicle during this 65-second period using the velocities at the beginning of the time intervals. We can do this by approximating the area under a curve. But what curve? In this case, imagine that the velocity of the vehicle is a function of time, v(t). We do not have this function, but we do have the values of th function at certain points in time. If we assume the function (the velocity) is constant between these points in time (which is not actually true), we can get an approximation. distance traveled - feet Give another estimate using the velocities at the end of the time periods. distance traveled feet Question Help: Video 20210110 2205M2 ing 20210110 220552 jpgarrow_forwardAsaparrow_forwardThe motion of a particle which moves along the straight line is defined by the relation x(t) = t3 - 9t? + 24t – 8, where x and t are expressed in meters and seconds respectively. Note that the coefficients of t have dimensions accordingly. (a) Determine when the velocity of the particle is zero. (b) Calculate the position vector and distance travelled by the particle when the acceleration is zero. Consider that at the starting point time t = 0 sec. (c) Does the particle move at constant velocity or constant acceleration? Justify your answer.arrow_forward
- An object's position in the as a function of time obeys the equation; x (t) = 3t – 2t³ + 1.5t where all constants have proper SI Units. What is the speed of the object in the x direction at t = 1.75 seconds?arrow_forwardThe displacement of a particle is given by s = 2t³ - 40t² + 84t - 54 where s is in feet and t is in seconds. Plot the displacement, velocity, and acceleration as functions of time for the first 16 seconds of motion. After you have made the plots, answer the questions. Questions: At t = 2.5 sec, At t = 9.3 sec, At t = 11.8 sec, S = S = S = M The velocity is zero when t = i ft, v = ft, v = ft, v = i i sec and when t = ft/sec, a = ft/sec, a = ft/sec, a = i MO i sec ft/sec ft/sec² ft/secarrow_forwardThe position y of a particle moving along the y axis depends on the time t according to the equation y = at- bť. The dimensions of the quantities a and b are respectively: Select one O LT, L/T? O LT?, L2T O None of these O LT, LT2 O T. TLarrow_forward
- A person takes a trip, driving with a constant speed of 96.5 km/h, except for a 20.0-min rest stop. The person's average speed is 67.0 km/h. (a) How much time is spent on the trip? 1.03 Your incorrect answer may have resulted from roundoff error. Make sure you keep extra significant figures in intermediate steps of your calculation. h (b) How far does the person travel? 67.23 Your incorrect answer may have resulted from roundoff error. Make sure you keep extra significant figures in intermediate steps of your calculation. kmarrow_forwardThe displacement of a particle is given by s=4t³-67t2 + 103t-66 where s is in feet and t is in seconds. Plot the displacement, velocity, and acceleration as functions of time for the first 14 seconds of motion. After you have made the plots, answer the questions. Questions: Att 3.7 sec, S= i Att - 6 sec, Att 10.1 sec, S= i SH i The velocity is zero when t = ft, v= i ft, v= i ft, v= i sec and when t= i ft/sec, a i ft/sec, a i ft/sec, a i sec ft/sec ft/sec ft/sec²arrow_forwardThe velocity of a particle is given by the function v(t)=t^2-7t+1027 , where the velocity is measured in meters per second. Determine the total displacement of the particle and the total distance travelled by the particle in the first ten seconds of its travel. Give exact answers, and provide units on your final answer.arrow_forward
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning