Question

Car A goes along a curve of 100 m radius at a speed of 10 m/s and increasing at the rate of 5 m/s2 whereas Car B is moving along a straight stretch of road with a velocity of 18.5 m/s and increases at a rate of 2 m/s2. The position of both cars A and B at a particular instant is as shown in Figure Q2(a). Calculate the acceleration of car A relative to car B and their relative direction.

Answer 1

2 Car A u having in having contripetal acelerations q=v² cava To I m/s2 11 TOO and tangential al acceleration ak D) 5 m/2 - at 20 ac 64° ed atx 20 asis a los co= a los 45 component of at along 5 hos 45 = 5 m/s2 2 component of ac along x ani act 11 ac los 45 = m/s². ñ m/s2 along xaci. 1 net acceleration (of A) 2 - 1 / 2 m/s m/y² = 4 m/g² 2 = 2√2 m/s

Component of at along ancis at Sino = 5 Sm 45=-5 m/s² Vz ياما Component of ac along y asis ac suso = i sin 45 1 m/s² 2 net accelerations of A along y 11 -5 - - 6 m/s2 = = -3√2 m/s2 Vz Vz a = Total acceleration of A (worot rent frame). (as Qr2 i +-352 } ] m/s² + 2 î m/s² a = Total acceleration of Car B = (woroto rest frame) Acceleration of cor a relative to CerB Ano analog (2.520 ? - 352 }) - (2²) (Q 12-2) î - 3v2 ŷ molsh magnitude la Asl = √ (222-2)² + (352) 2 = √4 (32-1) + 9x2 4 (2-252 + 1) + 18 12 - 812 + 18 | 30-852 = 4.323 m/s²

direction tand -352 - 3√2 f = tant ar2-2 282 2 11 - 78.951 79.951° clockwise to the asis.