c) Prove Newton's equations of motion at constant acceleration. That is,show thatI.II.III.Question 5v=u+at2s = ut ++at²v² = u² + 2aSd) Will an object moving in a circular track have zero acceleration?Explain-3 ma) Plot a displacement time graph for the diagram below.-2 m4 s-1 mO8t=01 m3s2 m1s3 m2 s4 m5 m

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Description: c) Prove Newton's equations of motion at constant acceleration. That is,show thatI.II.III.Question 5v=u+at2s = ut ++at²v² = u² + 2aSd) Will an object moving in a circular track have zero acceleration?Explain-3 ma) Plot a displacement time graph for

Velocity is the rate of change of position with respect to time. Its unit is m/s. The acceleration…

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c) Prove Newton's equations of motion at constant acceleration. That is, show that I. II. III. Question 5 v=u+at 1 s = ut + = at ² 2 v² u² + 2aS h d) Will an object moving in a circular track have zero acceleration? Explain -3 m a) Plot a displacement time graph for the diagram below. 4s -2 m -1 m O 8 t=0 1 m 3 s 2m 1s 3 m 2 s 4 m 5 m

c) Prove Newton's equations of motion at constant acceleration. That is, show that I. II. III. Question 5 v=u+at 1 s = ut + = at ² 2 v² u² + 2aS h d) Will an object moving in a circular track have zero acceleration? Explain -3 m a) Plot a displacement time graph for the diagram below. 4s -2 m -1 m O 8 t=0 1 m 3 s 2m 1s 3 m 2 s 4 m 5 m

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter2: Motion In One Dimension

Section: Chapter Questions

Problem 53P: A model rocket is launched straight upward with an initial speed of 50.0 m/s. It accelerates with a...

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An object moves with constant acceleration 4.00 m/s2 and over a time interval reaches a final velocity of 12.0 m/s. (a) If its original velocity is 6.00m/s, what is its displacement during the time interval? (b) What is the distance it travels during this interval? (c) If its original velocity is 6.00 m/s, what is its displacement during this interval? (d) What is the total distance it travels during the interval in part (c)?
A model rocket is launched straight upward with an initial speed of 50.0 m/s. It accelerates with a constant upward acceleration of 2.00 m/s2 until its engines stop at an altitude of 150. m. (a) What can you say about, the motion of the rocket alter its engines stop? (b) What is the maximum height reached by the rocket? (c) How long after liftoff does the rocket reach its maximum height? (d) How long is the rocket in the air?
Standing at the base of one of the cliffs of Mt. Arapiles in Victoria, Australia, a hiker hears a rock break loose from a height of 105 m. He can't see the rock right away but then does, 1.50 s later. (a) How far above the hiker is the rock when he can see it? (b) How much time does he have to move before the rock hits his head?
A car travels along a straight line at a constant speed of 60.0 mi/h for a distance d and then another distance d in the same direction at another constant speed. The average velocity for the entire trip is 30.0 mi/h. (a) What is the constant speed with which the car moved during the second distance d? (b) What If? Suppose the second distance d were traveled in the opposite direction; you forgot something and had to return home at the same constant speed as found in part (a). What is the average velocity for this trip? (c) What is the average speed for this new trip?
PROBLEM A race car starting from rest accelerates at a constant rate of 5.00 m/s2, (a) What is the velocity of the car after it has traveled 1.00 102 ft? (b) How much time has elapsed? (c) Calculate the average velocity two different ways. STRATEGY Weve read the problem, drawn the diagram in Figure 2.16, and chosen a coordinate system (steps 1 and 2). We'd like to find the velocity v after a certain known displacement x. The acceleration a is also known, as is the initial velocity v0 (step 3, labeling, is complete), so the third equation in Table 2.4 looks most useful for solving part (a). Given the velocity, the first equation in Table 2.4 can then be used to find the time in part (b). Part (c) requires substitution into Equations 2.2 and 2.7, respectively. Figure 2.16 (Example 2.4) SOLUTION (a) Convert units of x to SI, using the information in the inside front cover. Write the kinematics equation for v2 (step 4): Solve for v, taking the positive square root because the car moves to the right (step 5): Substitute v0 = 0, a = 5.00 m/s2, and x = 30.5 m: 1.00 102ft = (1.00 102 ft) v2 = v02 + 2a x v = v02+2ax v = v02+2ax = (0)2+2(5.00m/s2)(30.5m)= 17.5 m/s (b) Find the trooper's speed at that time. Substitute the time into the troopers velocity equation: vtrooper = v0 + atrooper t = 0 + (3.00m/s2)(16.9s) = 50.7 m/s Solve Example 2.5, Car Chase, by a graphical method. On the same graph, plot position versus time for the car and the trooper. From the intersection of the two curves, read the time at which the trooper overtakes the car.
A catapult launches a test rocket vertically upward from a well, giving the rocket an initial speed of 80.0 m/s at ground level. The engines then Fire, and the rocket accelerates upward at 4.00 m/s2 until it reaches an altitude of' 1 000 m. At that point, its engines fail and the rocket goes into free fall, with an acceleration of 9.80 m/s2, (a) For what time interval is the rocket in motion above the ground? (b) What is its maximum altitude? (c) What is its velocity just before it hits the ground? (You will need to consider the motion while the engine is operating and the free-fall motion separately.)
An express train passes through a station. It enters with an initial velocity of 22.0 m/s and decelerates at a rate of 0.150 m/s2 as it goes through. The station is 210 m long. (a) How long is the nose of the train in the station? (b) How fast is it going when the nose leaves the station? (c) If the train is 130 m long, when does the end of the train leave the station? (d) What is the velocity of the end of the train as it leaves?
Professional 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 a heartbeat?
Physics Review A hockey player strikes a puck, giving it an initial velocity of 10.0 m/s in the positive x-direction. The puck slows uniformly to 6.00 m/s when it has traveled 40.0 m. (a) What is the pucks acceleration? (b) At what velocity is it traveling after 2.00 s? (c) How long does it take to travel 40.0 m? (See Section 2.5.)
A river flows with a steady speed v. A student swims upstream a distance d and then back to the starling point. The student can swim at speed c in still water. (a) In terms of d, v, and c, what time interval is required for the round trip? (b) What time interval would be required if the water were still? (c) Which time interval is larger? Explain whether it is always larger.
There is a 250-m-high cliff at Half Dome in Yosemite National Park in California. Suppose a boulder breaks loose from the top of this cliff. (a) How fast will it be going when it strikes the ground? (b) Assuming a reaction time of 0.300 s, how long will a tourist at the bottom have to get out of the way after hearing the sound of the rock breaking loose (neglecting the height of the tourist, which would become negligible anyway if hit)? The speed of sound is 335 m/s on this day.
An object moves with constant acceleration 4.00 m/s2 and over a lime interval reaches a final velocity of 12.0 m/s. (a) If its initial velocity is 6.00 m/s, what is its displacement during the time interval? (b) What is the distance it travels during this interval? (c) If its initial velocity is -6.00 m/s, what is its displacement during points, (d) Does the change in speed of the downward-moving rock agree with the magnitude of the speed change of the rock moving upward between the same elevations? (e) Explain physically why it does or does not agree.