A particle $P$ leaves a fixed point $O$ and moves in a straight line so that, $t$ s after leav

Question

A particle $P$ leaves a fixed point $O$ and moves in a straight line so that, $t$ s after leaving $O$, its velocity is given by $v = -3t^2 + kt + 15$, where $k$ is a constant. Given that its velocity is $11$ ms${}^{-1}$ when $t = 2$, find the value of $k$. Find the value of $t$ for which the particle is at instantaneous rest. Find the maximum velocity of the particle. Calculate the total distance travelled by the particle in the first $4$ seconds. Find the time the particle returns to point $O$.

Accepted Answer

(a) $k=4$. (b) $t=3$ s. (c) Maximum velocity $=\frac{49}{3}\text{ m s}^{-1}$. (d) $44$ m. (e) $t=5$ s.

Kinematics - Maximum and Minimum Motion Quantities

Kinematics - Maximum and Minimum Motion Quantities

Video Solution:

Solution:

Solution locked