A particle $P$ starts from rest at a fixed-point $O$ and moves in a straight line. The accelerat

Question

A particle $P$ starts from rest at a fixed-point $O$ and moves in a straight line. The acceleration, $a$ ms${}^{-2}$, of the particle, $t$ s after passing through $O$ is given by $a = 8 - ct^2$, where $c$ is a positive constant. The velocity of the particle is $10$ ms${}^{-1}$ after $2$ seconds. Find the value of $c$, the time at which $P$ will change its direction of motion, the average speed of the particle in the first $5$ seconds.

Accepted Answer

(a) c=9/4; (b) t=sqrt(32/3) s = 3.27 s; (c) 2873/240 m s^{-1} = 12.0 m s^{-1}.

Kinematics - Velocity from Acceleration

Kinematics - Velocity from Acceleration

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