physic help vector plz ASAP?

Question

as a traffic light turns green, a waiting car starts with a constant acceleration of 6.0m/s^2. At the instant the car begins to accelerate , a truck with a constant velocity of 21m/s passes in the next lne(hint/: set the two distance equations equal to each other)
plz ansdwer step by step and show the work then you will get 10 free pts thx
a. how far will the car travel before it overtakes the truck
b how fast will the car be traveling when it overatakes the truck?
2. a stone falls freely from rest for 8.0s.
a. calculate the stone's velocity after 8.0s
b what is the stones displacement during this time?
3. a student drops a rock from a bridge to the water 12.0m below with what speed does the rock strick the water?

Answer 1

1. a) s_truck = 21 t
s_car = 1/2 (6.0) t^2 = 3.0 t^2
3.0t^2 = 21 t
=> t = 0 or 3.0t = 21 => t = 7.0 sec.
s = 3.0(7^2) = 147m.

b) v = 6.0 t = 42 m.


2. a) v = 9.81 t = 78.5 m/s.
b) s = t . (v+u)/2 = 8.0 (78.5/2) = 314 m.


3. v^2 = u^2 + 2as
=> v^2 = 2(9.81)(12.0) = 235.44
=> v = 15.3 m/s.

Answer 2

Take the north course as x- axis and east as y-axis. Then the preliminary speed is 50i and extremely final speed is -50j. The exchange in speed = -50j-50i. So, once you will plot it interior the co-ordinate axis this is alongside south- west. The fee is 70 as you have already guessed. (P. S. - i and j are unit vectors alongside x and y -axis)