Danica traveling at a speed of 200 km/hr on a straight road applies brakes to her car at point A and reduces her speed at a uniform rate to 150 km/hr at C in a total distance of 300 meters. a) Calculate the magnitude and direction of the total acceleration of her car immediately after she passes point B.

Danica traveling at a speed of 200 km/hr on a straight road applies brakes to her car at point
A and reduces her speed at a uniform rate to 150 km/hr at C in a total distance of 300 meters.
a) Calculate the magnitude and direction of the total acceleration of her car immediately after she passes point B. Assume BC to be a part of a circular path. [So, AB is a straight
line while BC is a circular arc.] (20)
b) Compute the time she took to go from A to C. (15)
P
X
Y
O
r
θ
A disc from point O (as shown) is launched at time t = 0 with an initial speed u at an angle β (0°< β
0), and a deceleration in the x-direction which is proportional to the horizontal
component of its velocity at any instant. Precisely, given this information, one can write the acceleration
of the disc as ⃗ where ̈ ̇ (i.e. q is some positive real number). i, j are the standard Cartesian unit vectors.
Find expressions for instantaneous position vector and velocity vector of the disc as functions of time t.
Justify whether or not the path of the disc in the medium would be parabolic. (20+20+5)
Y
X O
u
β
Medium