Distance in nth second

4 A particle \(P\) travels in the positive direction along a straight line with constant acceleration. \(P\) travels a distance of 52 m during the 2 nd second of its motion and a distance of 64 m during the 4th second of its motion.

1. Find the initial speed and the acceleration of \(P\).
2. Find the distance travelled by \(P\) during the first 10 seconds of its motion.

2. A car moves along a straight horizontal road with constant acceleration \(a \mathrm {~ms} ^ { - 2 }\) where \(a > 0\) The car is modelled as a particle. At time \(t = 0\), the car passes point \(A\) and is moving with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) In the first three seconds after passing \(A\) the car travels 20 m . In the fourth second after passing \(A\) the car travels 10 m . The speed of the car as it passes point \(B\) is \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) Find the time taken for the car to travel from \(A\) to \(B\).
(8)

2. A motorbike is moving with constant acceleration along a straight horizontal road. The motorbike passes a point \(P\) and 10 seconds later passes a point \(Q\). The speed of the motorbike as it passes \(Q\) is \(28 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) Given that \(P Q = 220 \mathrm {~m}\),

1. find the acceleration of the motorbike,
2. find the distance travelled by the motorbike during the fifth second after passing \(P\) VILV SIHI NI IIII M I ON OC
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