Two particles, $A$ and $B$, leave a point $O$ at the same time and initially travel in the sam

Question

Two particles, $A$ and $B$, leave a point $O$ at the same time and initially travel in the same direction along the same straight line. Particle $A$ starts with a velocity $3 \frac{1}{3} m s^{-1}$ and moves with a constant acceleration of $4 \frac{1}{3} m s^{-2}$. Particle $B$ starts with a velocity of $8 m s^{-1}$ and moves with an acceleration of $a m s^{-2}$, where $a = 3 - 2t$ and time $t$ is the time in seconds after passing point $O$. Find the velocity of each particle in terms of $t$, the displacement of each particle in terms of $t$. Hence, find the distance travelled by Particle $B$ in the first $6$ seconds, the distance from $O$ at which $A$ collides with $B$.

Accepted Answer

(a) $v_A=\dfrac{10+13t}{3}$, $v_B=8+3t-t^2\text{ m s}^{-1}$; (b) $s_A=\dfrac{10t}{3}+\dfrac{13t^2}{6}$, $s_B=8t+\dfrac32t^2-\dfrac13t^3\text{ m}$; (c) $\dfrac{41\sqrt{41}}6-\dfrac32\text{ m}$; (d) $\dfrac{94}{3}-\sqrt{15}\text{ m}$

Kinematics - Velocity from Acceleration

Kinematics - Velocity from Acceleration

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