Q4. A car travelling along a straight horizontal road takes 170s to travel between two sets of traffic lights at A
and B which are 2125m apart. The car starts from rest at A and moves with constant acceleration until it
reaches a speed of 17ms-1. The car then maintains this speed before moving with constant deceleration,
coming to rest at B. The magnitude of the deceleration is twice the magnitude of the acceleration.
(a) Sketch a speed-time graph for the motion of the car between A and B.
(3)
(b) Find the deceleration of the car.
(7)
(Total for question = 10 marks)

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

246

step-by-step explanation: