H1.02. 2022 Kinematics Answers to Examples, Quizzes Mini-tests

Answers to Examples, Quizzes & Mini-test [Kinematics] Quiz A cyclist riding at 7 m s-1 sees a stop sign and comes to a complete stop in 4 s. He then, in 6 s, returns to a speed of 5 m s-1. Which of the following shows his motion diagram? Solution: Answer is either B or C based on the relative directions of the acceleration and velocity vectors. Since the cyclist is slowing down in the first part of his motion, the acceleration and velocity vectors should be in opposite directions. Since he speeds up after the stop, the acceleration and velocity vectors should be in same direction. Answer is B not C because the final velocity is smaller than the initial velocity, so the last arrow should be shorter than the first arrow. Quiz The graph of velocity against time for a moving object is shown. Which of the following is the corresponding graph of displacement against time? (N95/I/5) A B C D

Solution: Answer: C • Velocity is always +ve, hence gradient of s-t graph should be always +ve (i.e. should neither be -ve nor zero). Eliminate A & B. • Velocity doesn’t change abruptly, so eliminate D where ‘sharp’ points indicate abrupt change in gradient and thus abrupt changes in velocity. MINI-TEST 1 A car is travelling along a straight road at a constant velocity initially for 1 minute. After that, the driver steps on the accelerator, causing the car’s speed to increase uniformly for 30 s. It then travels at constant velocity again for another minute before the driver slows down uniformly for 30 s to a momentary stop and then makes a U -turn back with the same acceleration for 30 s. Sketch the displacement -time, velocity -time and acceleration -time graphs to illustrate the motion of the car. My solution: t/s velocity t/s 60 90 150 180 210

Quiz 1) A ball is thrown vertically upwards. While the ball is in free fall, its acceleration A) increase, B) decrease C) remain constant 2) After a ball is thrown vertically upward and is in air, its speed A) increases, B) decreases, C) decreases and then increases, D) remains the same. Solution: Answer: Both (C) Quiz A stone is thrown upwards from the top of a cliff. After reaching its maximum height, it falls past the cliff- top and into the sea. The graph below shows how the vertical velocity v of the stone varies with time t after being thrown upwards. R and S are the magnitudes of the areas of the two triangles. Solution: What is the height of the cliff-top above the sea? (N98/I/3) A) R B) S C) R+ S D) R - S

Quiz Would a more massive object (e .g. elephant) fall faster than a less massive object (e .g. mouse) in a vacuum? Solution: All objects under free fall accelerates at 9.81 m s-2. Hence both objects speed up from rest at the same rate (speed increases by 9.81 m s-1 per second). MINI-TEST 2 A tennis ball is dropped from a height of 2.0 m above a hard level floor and it rebounds to a height of 1.5 m. From the instant it is released to the point where it reaches maximum height after the first bounce, (a) calculate the speed just after impact with the floor; (b) calculate the total time taken and; (c) sketch the velocity-time graph for this entire motion. My solution: (a) Take upwards as positive v = 0 m s-1 s = 1.5 m a = - 9.81 m s -2 Using v2 = u2 + 2as (0)2 = (u)2 + 2(- 9.81)(1.5) u = 5.42 m s -1 (b) Take upwards as positive Before bounce: After bounce: u = 0 m s-1 u = 5.42 m s-1, v = 0 (at highest point) s = -2.0 m s = 1.5 m a = -9.81 m s -2 a = -9.81 m s -2 Using s = ut + ½ a t2 v = u + at -2.0 = 0 + ½ (-9.81) t2 0 = 5.42 + (-9.81)t t = 0.639 s t = 0.552 s Total time = 0.639 + 0.552 = 1.19 s After bounce 1.5 m start 2.0 m Before bounce

(c) Take upwards as positive. Calculation of v just before the bounce: Using v2 = u2 + 2as v2 = 0 + 2 (-9.81)(-2.0) v = - 6.26 m s-1 Quiz For the scenario of a ball being projected in a parabolic path from point A, draw vectors to represent the displacement, velocity and acceleration at positions A, B, C, D and E. • Same sign convention is used for the graph. • The gradient of the two segments are the same. And the areas bounded by the graph and the x- axis are not.

MINI-TEST 3 1. A grasshopper jumps at an angle of 30 to the horizontal with a take-off speed of 3.0 m s-1. (a) What is the height of its jump? (b) How long is it above the ground? (c) What is the range of its jump? 2. A projectile is fired from the top of a cliff with a velocity of 150 m s-1 at 30⁰ to the horizontal as shown in the diagram. If the time of flight is 22.5 s, what is the height of the cliff? 3. A tennis ball is thrown horizontally at 10 m s-1 from a height of 2.0 m above flat horizontal ground. How far away from the thrower does it first hit the ground? My solutions: 1.

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Quiz The diagram shows the parabolic path of a ball thrown in air. On the same diagram, draw the path of the ball if air resistance is not negligible. Solution: ➔ Knowledge that both horizontal & vertical velocities are affected. Horizontal velocity decreases to ZERO (if flight time is long enough). ➔ Asymmetric (horizontal distance travelled per unit time DECREASES due to horizontal deceleration), reaches maximum height earlier, lower maximum height, shorter range