Question

12-10. Car A starts from rest at t-0 and travels along a straight road with a constant acceleration of 3 m/s until it reaches a speed of 27 m/s. Afterwards it maintains this speed. Also, when-0, car B located 2000 m down the road is traveling towards A at a constant speed of 20 m/s. Determine the distance travelled by car A when they pass each other. 20 m/s 2000 m 12-11. A particle travels along a straight line with a velocity v (12 -3r ) m/s, where t is in seconds. Whent 1 s, the particle is located 10 m to the left of the origin. Determine the acceleration when t-4 s, the displacement from t-O tot-10 s, and the distance the particle travels during this time period. 12-12. A sphere is fired downwards into a medium with an initial speed of 27 m/s. If it experiences a deceleration of a = (-6) ms, where t s in seconds, determine the distance travelled before it stops. 12-13. A particle travels along a straight line such that in 2 s it moves from an initial position SA = +0.5 m to a position SB =-1.5 m. Then in another 4 s it moves from SB to Sc = +2.5 m. Determine the particle's average velocity and average speed during the 6 s time interval. 12-14. A particle travels along a straight-line path such that in 4 s it moves from an initial position SA-8 m to a position Ss +3 m. Then in another 5 s it moves from SB to Sc--6 m. Determine the particle's average velocity and average speed during the 9 s time interval. 12-15. Tests reveal that a normal driver takes about 0.75 s before he or she can react to a situation to avoid a collision. It takes about 3 s for a driver having 0.1 % alcohol in his system to do the same. If such drivers are traveling on a straight road at 54 km/h (15m/s) and their cars can decelerate at 0.6 m/s, determine the shortest stopping distance d for each from the moment they see the pedestrians. Moral: If you must drink, please don't drive!

Answer 1

Please find the attached detailed solution.

Solution: 2-fo lel distance toavelled 42om/ Cars A 2000 m --> Both as toavel olistmce in time t u-o Coest) 2 2 Cos 8, speedl 2000 3 2ot 3t2 t4ct-yooo-o 2 t-30 , 4 5 seconds t=30, 4 5 Seconds time when both s pasS each tine (n't be Cmeglectedl others) 2 2 c Distemte tvlled by c each othes) A when they pass

Solution : ǐ2-11 V-72-32- cltt c=-21 tsec Displacement fsom t-o to t-10 sec Sto オ。 3 dispAcerresに20-S,--880 meke To Gal culahe disernce, fisst check when velboity bm eCome C o to to seconds is agped 16+ 896

Son2 sphese fised do wowasred Decelentiont m/s velocity (y Applyine Neton's law Cit stops Also,tat Pudt i 272二12ts 2 8 5378 verses 2x2 29 Distne it toavels befose it stops) So).thon : r2-13 1m 2sec. Sa- to‘5m, to SRE-f.5 Avenge velocity 224B 214 Avestgg velocity08 333 n/s

CoudAbsdute distxe .5to,5 +0.5 2 SpeaneAbslule 2 2.5m-D,625m Sec. 2147 2+2,5 Areage speed Aee velocty drong 5 sed 5 |Ave- ge velocity -f.ggg m/s eed olumma 4 sec . = .2m/s 5

en c Solution 12-15 Normal doives takes 0.5 se 3 sec. to oo.c4 0 , fヅ0 Alcohofdm.voS, bkes 54 kmh (15m/s) 2- t'= tto ,45 C o. Alcoho doires 2. time 2 2 s, 11. 25 m bme it is movimg ad constnt v o AlCobo 2. ohaiveb