Question

The performance of two different cars, car 1 and car 2, was measured on a long horizontal test track. Car 1 started from rest and ran with constant acceleration until it was halfway down the track and then stopped accelerating, continuing to run at the attained speed to the end of the track. Car 2 started from rest and ran with a constant acceleration for the entire distance. It was observed that both cars covered the test distance in the same amount of time. (a) What was the ratio of the average speed of car 1 to that of car 2? Vavg, 1 = Vavg, 2 (b) What was the ratio of the initial acceleration of car 1 to that of car 2? ai, 1 = ai, 2 (c) What was the ratio of the final speed of car 1 to that of car 2? VF, 1 = VF, 2

Answer 1

For Car 1 td/ d/ Let the length of the track be do let the total taken by the car is 't Given Initial velocity, u=0 at is accelerated upto the let it reaches to maximum Let the time taken to cover a and time taken to cover half distance dla velocity v accelerated distance be unaccelerated distance t2 for Then, t = 2 – (D the first half distance : using u?-u? = zas 12 = 2 axd az v2 - W using , rautat r= axt, V= V2 xti

Now, torte - t d av d -t a 20 st 2v av Tv= d alow, titte=t d td -t a t=d 2v or vad so, the final velocity, Acceleration, ae = a = ela वर olt e Average velocity is given by a Displacement Time interval Vargit d Vargit =

For Car 2 Initial velocity, uno Time - t using x= ht that? ad using raurat vpap 20 x t =) ta

Part a) soln. dib aug, 1 Vay, 2 ang, I ang, Part by seln ais ai, 2 } Part c) sela d/t 11 V2