Mathematics AI: KINEMATICS, RELATIVE VELOCITY Topical Past Paper Questions

[Maximum mark: 14] At an outdoor ballpark for children, a ball is launched from the ground, with initial speed $ 12 \, \text{m} \, \text{s}^{-1} $ and initial launch angle $ \theta $ to the horizontal ground, where $ 0 The ball can be modelled as a projectile, using $ \left(\begi…

[Maximum mark:4] Two model cars are driving along the same straight track. Car A leaves point O at $t=0$ and its displacement $(x_{A}^{\prime}$ metres) from O at $t$ seconds is given by the equation $$ x_{A}=4\sqrt{t},\mathrm{f o r}0\leq t\leq9. $$ A faster car, B, leaves O at $t…

[Maximum mark: 8] The velocity v of a particle at time t, as it moves along a straight line, can be modelled by the piecewise function $$ \nu(t)=\left\{\begin{aligned}&u_{1}(t),&0\leq t\leq T\\ &u_{2}(t),&t\geq T\end{aligned}\right. $$ where $ u_{1}(t)=2t^{2}-t^{3} $ and $ u_{2}(…