The figure shows the position vs. time graphs of two objects A and B moving along x-axis for 5 seconds.

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1 Velocity from position vs. time graph The figure shows the position vs. time graphs of two objects A and B moving along x-axis for 5 seconds. (a) Do objects A and B moving along a straight line? Explain? x (m) A B (b) What is the speed of B at t = 3 s? Is it same at 4 s? Velocity? Show calculation for at least one time. (Ans: speed of B at 3s is 2.5 m/s) t (s) (c) Do objects A and B ever have same speed? If so what times explain? (d) If +x is east, what direction object A is moving around t = 1 s? Explain. (e) At around t = 2.5 s, is the speed of A greater than, less than, or equal to the speed of B? Explain. (f) Are either of object A or B accelerating? If so which one or both of them? Explain.

2 Sketching Velocity vs time Graphs Suppose the car shown in the sketch can move back and forth in a straight line. Assume the positive - 0 direction is to the right. Now sketch the velocity vs time graph for the following cases and explain briefly why it make sense. 1. The car is moving to the right with constant 2. The car is initially moving to the right but after a velocity from origin. while reverses the direction The car is moving from right to the left towards the origin at constant velocity. 4. The car moves from far left to the right at constantly increasing speed. 5. The car is not moving at all.

3 Sketching Acceleration vs time Graphs: Suppose the car shown in the sketch can move back and forth in a straight line. Assume the positive direction is to the right. Now sketch the acceleration vs time graph for the following cases and explain briefly why it make sense The car moves to the right from origin, speeding up at steady (constant) rate. 2. The car moves to the left from origin, speeding up at steady rate The car moves from right to the left towards the origin at constant velocity. 4. The car moves from far left to the right, slowing down at steady rate. 5. The car moves towards the right at constant velocity.

4 Displacement from v-t graph 1. What was the objects average acceleration first 8 s? (Ans: 0.75 m/s 2 ) v x (m/s) Velocity vs. time graph of an object moving in 1D. x0 = t (s) Draw position vs time graph from above graph. 2. How far did the object move in first 8 s? (Ans: 28 m) 3. What was the average speed in first 8 s? (Ans: 3.5 m/s)

5 Motion Along Inclined Line The ball shown in the sketch is rolling downhill. The positions are recorded at equal time intervals. Is the speed increasing or decreasing? Sketch the velocity vectors for each positions. Using any two convenient velocity vectors, draw v 2 v. 1 What is the direction of acceleration? Uphill or downhill? Next assume the ball was rolled uphill. Does the ball slow down going uphill? Draw velocity vectors for each position. Find the direction of acceleration when the ball is climbing uphill using the same method that was used for downhill motion. Is the direction of acceleration uphill or downhill?

6 Rolling Ball Kicked and a Falling Ball A kicked soccer ball is rolling from point p to point q on a horizontal surface with constant velocity, vo. When the ball reaches to point b, it receives a swift kick in the direction perpendicular to the vo. If the ball was not rolling the kick would have provided a speed v in the direction of kick. Since the ball is rolling, what is the path followed by the ball after the kick? p q (Hint: Draw vo and v and find sum) Direction of kick Find the direction of change in velocity by using vector subtraction. What is the direction of acceleration at the moment the ball receives the kick? 0 A ball is in free fall after being dropped from 0 m position. The positions of the ball are recorded at 1 s interval. Smallest division on the scale is 1m. Estimate the acceleration of the 1 2 ball at least two different position using y y0 v0 yt ayt. 2 (Ans: For first sec 10 m/s2) 10 Are the accelerations nearly same (constant)? Now draw the displacement vectors by drawing arrows from one ball to next and so on. Is the velocity changing? Draw velocity vectors to the left of position vectors. Is acceleration up or down? Next draw the approximate positions of a ball thrown up. Numbers not needed. Use those positions to find the direction of acceleration just like you did for a falling ball. Is acceleration up or down for the freely rising ball? 80

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