First slide

Rectilinear Motion

Question

Each of the four particles move along an x-axis. Their coordinates (in metres) as function of time (in seconds) are given by
$\begin{array}{l} Particle 1: x (t) = 3.5 - 2.7 t^{3} \\ Particle 2 : x (t) = 3.5 + 2.7 t^{3} \\ Particle 3: x (t) = 3.5 + 2.7 t^{2} \\ Particle 4: x (t) = 3.5 - 3.4 t - 2.7 t^{2} \end{array}$
which of these particles is speeding up for t > 0?

Difficult

A

All four
B

only 1
C

only 1, 2 and 3
D

only 2, 3 and 4

Solution

$A t A = 0$
$\frac{d x}{d t} = 0 for particles 1, 2 and 3 and |\frac{d^{2} x}{d t^{2}}| > 0 for t > 0$
$and \frac{d x}{d t} = - 3.4 m / s for particle 4 and \frac{d^{2} x}{d t^{2}} is negative for t > 0$
$Therefore for t > 0; |\frac{d x}{d t}| is increasing in all.$

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