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9 A lion is watching a zebra from 35 m behind it. Both are stationary. The lion then starts chasing by accelerating at a constant rate of 3 ms2 for 5s. Once at top speed the lion decelerates at 0.5 ms. The zebra starts moving Is after the lion started, accelerating at a constant rate of 2 ms2 for 7s before maintaining a constant speed. a Show that the lion has not caught the zebra after 8s. b Show that the gap between them at times, for />8, after the start of the lion's motion is given by 7² - 51 +51 and, hence, determine when the lion catches the zebra, or when the lion gets closest and 4 2 how close it gets. 10 A car is behind a tractor on a single-lane straight road with one lane in each direction. Both are moving at 15 ms ¹. The speed limit is 25 m s¹, so the car wants to overtake. The safe distance between the car and the tractor is 20 m. a To overtake, the car goes onto the other side of the road and accelerates at a constant rate of 2 ms²² until reaching the speed limit, when it continues at constant speed. Show that the distance the car is ahead of the tractor at time is after it starts to accelerate is given by 1²-20 for 0 <1 ≤ 5, and deduce that the car is not a safe distance ahead of the tractor before reaching the speed limit. b The car pulls in ahead of the tractor once it is a safe distance ahead. Find the total time taken from the start of the overtaking manoeuvre until the car has safely overtaken the tractor. cTo overtake safely on the single-lane road, when the car returns to the correct side of the road in front of the tractor there must be a gap between the car and oncoming traffic of at least 20 m. Assuming a car travelling in the opposite direction is moving at the speed limit, find the minimum distance it must be from the initial position of the overtaking car at the point at which it starts to overtake.

9 A lion is watching a zebra from 35 m behind it. Both are stationary. The lion then starts chasing by accelerating at a constant rate of 3 ms2 for 5s. Once at top speed the lion decelerates at 0.5 ms. The zebra starts moving Is after the lion started, accelerating at a constant rate of 2 ms2 for 7s before maintaining a constant speed. a Show that the lion has not caught the zebra after 8s. b Show that the gap between them at times, for />8, after the start of the lion's motion is given by 7² - 51 +51 and, hence, determine when the lion catches the zebra, or when the lion gets closest and 4 2 how close it gets. 10 A car is behind a tractor on a single-lane straight road with one lane in each direction. Both are moving at 15 ms ¹. The speed limit is 25 m s¹, so the car wants to overtake. The safe distance between the car and the tractor is 20 m. a To overtake, the car goes onto the other side of the road and accelerates at a constant rate of 2 ms²² until reaching the speed limit, when it continues at constant speed. Show that the distance the car is ahead of the tractor at time is after it starts to accelerate is given by 1²-20 for 0 <1 ≤ 5, and deduce that the car is not a safe distance ahead of the tractor before reaching the speed limit. b The car pulls in ahead of the tractor once it is a safe distance ahead. Find the total time taken from the start of the overtaking manoeuvre until the car has safely overtaken the tractor. cTo overtake safely on the single-lane road, when the car returns to the correct side of the road in front of the tractor there must be a gap between the car and oncoming traffic of at least 20 m. Assuming a car travelling in the opposite direction is moving at the speed limit, find the minimum distance it must be from the initial position of the overtaking car at the point at which it starts to overtake.

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I need help with Question 9b and Question 10c. 

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9 A lion is watching a zebra from 35 m behind it. Both are stationary. The lion then starts chasing by accelerating at a constant rate of 3ms2 for 5s. Once at top speed the lion decelerates at 0.5 ms-2. The zebra starts moving Is after the lion started, accelerating at a constant rate of 2 ms for 7s before maintaining a constant speed. a Show that the lion has not caught the zebra after 8 s. b Show that the gap between them at time f s, for t> 8, after the start of the lion's motion is given by 51 - 51 + and, hence, determine when the lion catches the zebra, or when the lion gets closest and 4 2 how close it gets. 10 A car is behind a tractor on a single-lane straight road with one lane in each direction. Both are moving at 15 ms. The speed limit is 25 m s, so the car wants to overtake. The safe distance between the car and the tractor is 20 m. a To overtake, the car goes onto the other side of the road and accelerates at a constant rate of 2 ms-2 until reaching the speed limit, when it continues at constant speed. Show that the distance the car is ahead of the tractor at time rs after it starts to accelerate is given by r?- 20 for 0<r 5, and deduce that the car is not a safe distance ahead of the tractor before reaching the speed limit. b The car pulls in ahead of the tractor once it is a safe distance ahead. Find the total time taken from the start of the overtaking manoeuvre until the car has safely overtaken the tractor. c To overtake safely on the single-lane road, when the car returns to the correct side of the road in front of the tractor there must be a gap between the car and oncoming traffic of at least 20 m. Assuming a car travelling in the opposite direction is moving at the speed limit, find the minimum distance it must be from the initial position of the overtaking car at the point at which it starts to overtake.
Transcribed Image Text:9 A lion is watching a zebra from 35 m behind it. Both are stationary. The lion then starts chasing by accelerating at a constant rate of 3ms2 for 5s. Once at top speed the lion decelerates at 0.5 ms-2. The zebra starts moving Is after the lion started, accelerating at a constant rate of 2 ms for 7s before maintaining a constant speed. a Show that the lion has not caught the zebra after 8 s. b Show that the gap between them at time f s, for t> 8, after the start of the lion's motion is given by 51 - 51 + and, hence, determine when the lion catches the zebra, or when the lion gets closest and 4 2 how close it gets. 10 A car is behind a tractor on a single-lane straight road with one lane in each direction. Both are moving at 15 ms. The speed limit is 25 m s, so the car wants to overtake. The safe distance between the car and the tractor is 20 m. a To overtake, the car goes onto the other side of the road and accelerates at a constant rate of 2 ms-2 until reaching the speed limit, when it continues at constant speed. Show that the distance the car is ahead of the tractor at time rs after it starts to accelerate is given by r?- 20 for 0<r 5, and deduce that the car is not a safe distance ahead of the tractor before reaching the speed limit. b The car pulls in ahead of the tractor once it is a safe distance ahead. Find the total time taken from the start of the overtaking manoeuvre until the car has safely overtaken the tractor. c To overtake safely on the single-lane road, when the car returns to the correct side of the road in front of the tractor there must be a gap between the car and oncoming traffic of at least 20 m. Assuming a car travelling in the opposite direction is moving at the speed limit, find the minimum distance it must be from the initial position of the overtaking car at the point at which it starts to overtake.
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