How do you find the acceleration

Question

A car passes three posts P, Q and R, on a straight horizontal road. The distance PQ = 50m. The

distance QR = 100m. The car, moving with constant acceleration, takes 2 seconds to travel from P to Q

and 3 seconds to travel from Q to R.

(a) the acceleration of the car,

(b) the speed car at the instant it passes Q

Answer 1

0 to 50 takes 2 seconds

50 to 100 takes 3 seconds

constant acceleration

a(t) = c

v(t) = ct + k

s(t) = ct^2/2 + kt

s(2) = c4/2 +k2 = 50

c+k = 25

k =25-c

s(5) = c(25/2) +5k = 100

5c/2 +k =20

5c/2 +25-c =20

5c+50 -2c =40

3c = -10

c = -10/3

acceleration = a(t) = -10/3 = - 3 1/3 m/s^2

velocity at Q = v(2) = -10(2)/3 +85/3 = -20/3 +85/3 = 65/3 = 21 2/3 m/s