Multiple Choice 1. (A) X The graph to the left shows the velocity v as a function of time t for an object moving in a straight line. Which of the following graphs shows the corresponding displacement x as a function of time t for the same time interval? ia (D) x K
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- Suppose that a ball is thrown straight up in the air, and that a secondball is thrown straight upward two seconds after the first. It reaches thesame maximum height as the first ball, which is 6.00 m.a. What is the position of the first ball as a function of time, y1(t)?Take the initial height of the ball as y0 = 0.b. What is the position of the second ball as a function of time, y2(t)?Take the initial height of the ball as y0 = 0.c. Draw a y − t diagram of y1(t) and y2(t). Label the max heights, timeto max height for the first ball, and note the point corresponding to thetime and height of passing.d. When do the balls pass each other in the air? Assume the balls arebeing throw up adjacent to each other.e. At what height above y0 = 0 do the balls pass each other?f. Can you find the time of passing by just using the y − t diagram?Suppose that a ball is thrown straight up in the air, and that a secondball is thrown straight upward two seconds after the first. It reaches thesame maximum height as the first ball.a. What is the position of the first ball as a function of time, y1(t)?Take the initial height of the ball as y0 = 0.b. What is the position of the second ball as a function of time, y2(t)?Take the initial height of the ball as y0 = 0.c. Draw a y − t diagram of y1(t) and y2(t). Label the max heights, timeto max height for the first ball, and note the point corresponding to thetime and height of passing.d. When do the balls pass each other in the air? Assume the balls arebeing throw up adjacent to each other.e. At what height above y0 = 0 do the balls pass each other?f. Can you find the time of passing by just using the y − t diagram?2. A the are golf ball is hit horizontally edge of a cliff. Its. given as a) Compute the t = 0, 1, 2, 3 b) Determine acceleration. Solution: = 20t when = O when t = 1 X t = o 20(0 = functions (20 m.s') t 20(1) = 20 3 and the ball's and y of time by / and y sec. from y = -(4.9 m. 5²) +² coordinates at times. initial velocity and its y=-4.9t² y = -4.9 (0)² tee at coordinates y = - 4.9 (1) ² = -4.9 m
- A particle moving along a straight line will be s centimetres from a fixedpoint at time t seconds, where t > 0 and s = 27t^3 + 16/t + 10a. Determine when the velocity will be zero.b. Is the particle accelerating? Explain.An object is moving with constant non-zero acceleration in the +x direction. The position versus time graph of this object is O a horizontal straight line. a straight line making an angle with the time axis. a parabolic curve. O a vertical straight line.a.Members of the froghopper family of insects (family Cercopoidea) can accelerate from rest to 0.84 m/s in 5.80 ms. What is the acceleration (in m/s2)? Enter the numerical part of your answer, rounded to three significant figures. b.A western honey bee (Apis mellifera) flies 3.51 m north and then 6.31 m east. What is its displacement from the starting position? Enter only the numerical part of your answer (in m) to the nearest integer.
- During a video game, a point on the screen moved 16.6 cm in the positive y direction and then 13.6 cm in the negative x direction, all in a time of 4.2s. a. What was the point's average velocity during this time? (Magnitude only) b. What was its average speed?The position of a particle as a function of time is given by x(t) = (5.77 m/s²) t² - (2.99 m/s) t. %3D What is the velocity of the particle, in m/s, at t= 2.07 s? What is the acceleration of the particle, in m/s2, at t = 2.07 s? At what non-zero time, in seconds, is the velocity equal to zero? What is the maximum position of the particle in meters?You stand at the top of a deep well. To determine the depth, D, of the well you drop a rock from the top of the well and listen for the splash as the rock hits the water’s surface. The sound of the splash arrives t = 3.1 s after you drop the rock. The speed of sound in the well is vs = 336 m/s. A. Enter the quadratic equation for the distance, D, in terms of the time, the acceleration due to gravity, and the speed of sound. Arrange the expression so that the coefficient of the D2 term is 1. B. Solve the quadratic equation for the depth of the well, D, and calculate it's value, in meters.
- A bicycle rider travels 20,0 km north in 1.5 hours. She then turns directly south and travels 10.0 km in 1.0 hours. What is her average velocity In a time interval of 30,0 5, a car uniformly accelerates from 16.0 m/5 to 32.0 m/5. W A truck moves 100 km due south, then turn 180 degrees and drives 50 km due north. It’s displacement and distance travelled are ? A juggler throws a ball in an arc. At the top of its flight, the magnitude of the vertical velocity and acceleration are __ ms/a and __ m/s2 respectivelyConsider an object moving along a line with the given velocity v. Assume time t is measured in secondsand velocities have units of m/s.a. Determine when the motion is in the positive direction and when it is in the negative direction.b. Find the displacement over the given interval.c. Find the distance traveled over the given interval.v(t) = 50e-2t on [0, 4]The velocity function of a particle moving along a horizontal line is given by v(t) = t2-8t+15, where t >= 0 is in seconds. The particle is 5/3 units to the left of the origin at the second instant when it changes direction. 1. Determine th etime interval (s) on which the particle is both moving to the right and slowing down. 2. Find the position function of the particle.