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Initially, when the car passes the point P, it is moving with a constant speed of 16 ms¹. T seconds after passing P, the car begins to decelerate uniformly. 37 seconds after passing P, the car has speed 4 ms¹. At this instant, the magnitude of the car's deceleration changes. The car then decelerates uniformly until it comes to rest after a further T seconds. (a) Sketch a velocity-time graph representing the motion of the car after it passes P. (b) Find, in terms of T, the time at which the car has speed 8 ms¹. The car stops 133 metres from P. (c) Show that T=3.5.

Initially, when the car passes the point P, it is moving with a constant speed of 16 ms¹. T seconds after passing P, the car begins to decelerate uniformly. 37 seconds after passing P, the car has speed 4 ms¹. At this instant, the magnitude of the car's deceleration changes. The car then decelerates uniformly until it comes to rest after a further T seconds. (a) Sketch a velocity-time graph representing the motion of the car after it passes P. (b) Find, in terms of T, the time at which the car has speed 8 ms¹. The car stops 133 metres from P. (c) Show that T=3.5.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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PLese answer part (A) (b) and (c)

6 A car travels along a straight horizontal road. Initially, when the car passes the point P, it is moving with a constant speed of 16 ms¹¹. T seconds after passing P, the car begins to decelerate uniformly. 37 seconds after passing P, the car has speed 4 ms¹. At this instant, the magnitude of the car's deceleration changes. The car then decelerates uniformly until it comes to rest after a further T seconds. (a) Sketch a velocity-time graph representing the motion of the car after it passes P. (b) Find, in terms of T, the time at which the car has speed 8 ms¹. The car stops 133 metres from P. (c) Show that T = 3.5.
Transcribed Image Text:6 A car travels along a straight horizontal road. Initially, when the car passes the point P, it is moving with a constant speed of 16 ms¹¹. T seconds after passing P, the car begins to decelerate uniformly. 37 seconds after passing P, the car has speed 4 ms¹. At this instant, the magnitude of the car's deceleration changes. The car then decelerates uniformly until it comes to rest after a further T seconds. (a) Sketch a velocity-time graph representing the motion of the car after it passes P. (b) Find, in terms of T, the time at which the car has speed 8 ms¹. The car stops 133 metres from P. (c) Show that T = 3.5.
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