Exercise 1C

A cheetah is pursuing an impala. The impala is running in a straight line at a constant speed of 16 m/s. The cheetah is 10 m behind the impala, running at 20 m/s but tiring, so that it is decelerating at 1 ms -2. Find an expression for the gap between the cheetah and the impala t seconds later. Will the impala get away?

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Intro: In the savannah, a cheetah is chasing an impala. The impala runs at a constant speed of 16 m/s, with the cheetah initially 10 meters behind and running at 20 m/s but slowing down at 1 m/s². The question is, what will be the gap between them 7 seconds later, and can the impala … Read more

A freight train 1/4 km long takes 20 seconds to pass a signal. The train is decelerating at a constant rate, and by the time the rear truck has passed the signal it is moving 10 kilometres per hour slower than it was when the front of the train passed the signal. Find the deceleration in kilometre-hour units, and the speed at which the train is moving when the rear truck has just passed the signal.

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A freight train, spanning a length of 1/4km, requires 20 seconds to traverse a signal. The train undergoes a constant deceleration, and as the rear truck clears the signal, its speed is10 kilometers per hour less than it was when the front of the train initially passed the signal. The task at hand involves determining … Read more

A car travelling at 10 ms is 25 metres from a pedestrian crossing when the traffic light changes from green to amber. The light remains at amber for 2 seconds before it changes to red. The driver has two choices: to accelerate so as to reach the crossing before the light changes to red, or to try to stop at the light. What is the least acceleration which would be necessary in the first case, and the least deceleration which would be necessary in the second?

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Title: Traffic Dilemma: Acceleration and Deceleration Choices Introduction: In the urban rhythm, a car approaches a pedestrian crossing with the traffic light transitioning from green to amber. This scenario unfolds a critical decision for the driver: accelerate to clear the crossing before the light turns red or decelerate to a halt at the amber signal. … Read more

A cyclist comes to the top of a hill 165 metres long travelling at 5 m s, and free-wheels down it with an acceleration of 0.8 ms 2. Write expressions for his speed and the distance he has travelled after seconds. Hence find how long he takes to reach the bottom of the hill, and how fast he is then travelling.

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Title: Cyclist’s Descent: A Gravity-Powered Journey Introduction: Embarking on a gravity-powered journey, a cyclist conquers the ascent to the top of a hill, only to release the brakes and free-wheel down the slope. This numerical exploration unravels the dynamics of the cyclist’s descent, encompassing expressions for speed and distance over time, culminating in insights into … Read more

A boy kicks a football up a slope with a speed of 6 m s1. The ball decelerates at 0.3 m s 2. How far up the slope does it roll?

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“In this scenario, we encounter a boy kicking a football up a slope with an initial speed of 6 m/s. As the ball ascends, it undergoes deceleration at a rate of 0.3 m/s². Our objective is to determine the distance the ball travels up the slope before coming to a stop. Through the application of … Read more

A downhill skier crosses the finishing line at a speed of 30 m s1 and immediately starts to decelerate at 10 m s ̃2. There is a barrier 50 metres beyond the finishing line. (a) Find an expression for the skier’s speed when she is s metres beyond the finishing line. (b) How fast is she travelling when she is 40 metres beyond the finishing line? (c) How far short of the barrier does she come to a stop? (d) Display an (s, v) graph to illustrate the motion.

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Title: Downhill Descent: The Braking Skier’s Journey Introduction: Embarking on a thrilling downhill descent, a skier accelerates across the finishing line with a speed of 30 m/s. However, the journey doesn’t end there; an immediate deceleration ensues, dictated by the skier’s effort to safely navigate the terrain. This numerical exploration unveils the dynamics of the … Read more

An ocean liner leaves the harbour entrance travelling at 3 m s1, and accelerates at 0.04 m s2 until it reaches its cruising speed of 15 m s1. (a) How far does it travel in accelerating to its cruising speed? (b) How long does it take to travel 2 km from the harbour entrance?

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Title: Seafaring Acceleration: The Ocean Liner’s Voyage Introduction: Embarking on a maritime journey, an ocean liner sets sail from the harbour entrance with an initial velocity of 3 m/s. The vessel undergoes a calculated acceleration, propelling it to a steady cruising speed of 15 m/s. This numerical exploration delves into the liner’s acceleration phase, unveiling … Read more

A train travelling at 55 m s1 has to reduce speed to 35 ms to pass through a junction. If the deceleration is not to exceed 0.6 m s2, how far ahead of the junction should the train begin to slow down?

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Title: Strategic Deceleration: Train at the Junction Introduction: Navigating the intricacies of railway dynamics, this numerical exploration examines a scenario where a train, hurtling at 55 m/s, strategically adjusts its velocity to 35 m/s for a safe passage through a junction. The primary focus is on determining the critical distance at which the train must … Read more

A cyclist riding at 5 m s1 starts to accelerate, and 200 metres later she is riding at 7 m s’. Find her acceleration, assumed constant.

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Title: Cycling Acceleration Challenge Introduction: Embarking on a journey of acceleration, our cyclist’s pedal-powered adventure unfolds as she transitions from a cruising speed of 5 m/s to a sprightly 7 m/s. The crux of this numerical exploration lies in uncovering the acceleration experienced by the cyclist during this dynamic shift. Scenario Overview: Picture a cyclist … Read more

A motor-scooter moves from rest with acceleration 0.1 m s2. Find an expression for its speed, v m s1, after it has gone s metres. Illustrate your answer by sketching an (s, v) graph.

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Title: Acceleration Unveiled: Motor-Scooter Odyssey Introduction: Embarking on a journey from a state of rest, a motor-scooter gradually unfolds its accelerating prowess, attaining a velocity that intricately corresponds to the distance covered. This numerical exploration seeks to unveil the relationship between speed and distance for a motor-scooter accelerating at a consistent rate. Scenario Overview: Imagine … Read more