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(a) Speed of the car at 165 s = 25 – 25 * 5/20 = 25 – 6.25 = 18.75 m/s

(b) If x is the distance travelled by the motocycle from Point B to A,

d²x/dt² = 3

dx/dt = 3t + k         k is a constant

Assuming the speed of the motocycle is 0 at t =0, k = 0

x = 3t²/2 +   k1    Since at t =0, x=0, k1 =0

Distance travelled by the car from Point A to B = Area of the graph 

= (25 * 16)/2 + 25 * 144 + ( 25 * 20 )/2 = 200 + 3600 + 250 = 4050

At time T, the car and the motocycle met, the sum of the distance they travelled at time T is 4050

200 + 25  ( T – 16 ) + 3T²/2   = 4050

1.5T² + 25T -4250 = 0 (proved)

 

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