Answer to Question #217529 in Physics for jie

Question

a Motorbike is running initially with a speed of 180 m/s at a constant speed for 12secs, at which time BMW motorbike passes him at a speed of 240 m/s and still accelerating at 3m/s2 until it reaches the speed of 299m/s. The driver of the Ducati Motorbike accelerates uniformly and chases the BMW motorbike until he overtakes it. What is the acceleration needed for Ducati driver to overtake the other motorbike if he reaches a top speed of 399 m/s at the time of overtaking? What is the total distance covered by the Ducati Motorbike from its initial point?​

Answer 1

$$t_1=\frac{299-240}{3}=19.7\ s\\0.5(180+399)t=299(t-19.7)\\+240(19.7)+0.5(3)(19.7)^2\\t=61.1\ s$$

$$a=\frac{399-180}{61.1}=3.59\frac{m}{s^2}\\s=180(61.1)+0.5(3.59)(61.1)^2=17700\ m$$