A test sled $P$ starts from point $A$ at time $t=0$. At the same instant, a maintenance cart \

Question

A test sled $P$ starts from point $A$ at time $t=0$. At the same instant, a maintenance cart $Q$, $40$ metres ahead at $B$, moves in the same direction at a constant speed of $6\text{ m s}^{-1}$. The velocity of $P$ is $3t^2\text{ m s}^{-1}$. (i) Find the positions of $P$ and $Q$, measured from $A$, at time $t$. (ii) Show that $P$ catches $Q$ after exactly $4$ seconds and that this is the only positive catch time. (iii) Find the position of the catch and the relative speed at which $P$ closes on $Q$ at that instant.

Accepted Answer

(i) $x_P=t^3$, $x_Q=40+6t$; (ii) $t=4\text{ s}$ only; (iii) $64\text{ m from }A$, relative speed $42\text{ m s}^{-1}$

Test sled catches a moving cart

Test sled catches a moving cart

Solution:

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