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\includegraphics[max width=\textwidth, alt={}, center]{e69f8d73-764e-4f13-a126-faec02c4ad08-07_579_848_1142_242} The diagram shows a velocity-time graph representing the motion of two cars \(A\) and \(B\) which are both travelling along a horizontal straight road. At time \(t = 0\), car \(B\), which is travelling with constant speed \(12 \mathrm {~ms} ^ { - 1 }\), is overtaken by car \(A\) which has initial speed \(20 \mathrm {~ms} ^ { - 1 }\). From \(t = 0 \operatorname { car } A\) travels with constant deceleration for 30 seconds. When \(t = 30\) the speed of car \(A\) is \(8 \mathrm {~ms} ^ { - 1 }\) and the car maintains this speed in its subsequent motion.

1. Calculate the deceleration of \(\operatorname { car } A\).
2. Determine the value of \(t\) when \(B\) overtakes \(A\).
   \includegraphics[max width=\textwidth, alt={}, center]{e69f8d73-764e-4f13-a126-faec02c4ad08-08_293_773_354_246} A rectangular block \(B\) is at rest on a horizontal surface. A particle \(P\) of mass 2.5 kg is placed on the upper surface of \(B\). The particle \(P\) is attached to one end of a light inextensible string which passes over a smooth fixed pulley. A particle \(Q\) of mass 3 kg is attached to the other end of the string and hangs freely below the pulley. The part of the string between \(P\) and the pulley is horizontal (see diagram). The particles are released from rest with the string taut. It is given that \(B\) remains in equilibrium while \(P\) moves on the upper surface of \(B\). The tension in the string while \(P\) moves on \(B\) is 16.8 N .