Question

A particle moves along a straight line with equation of motion s = f(t), where s is measured in meters and t in seconds. Find the velocity and speed (in m/s) when t = 5. f(t) = 18 + 48/t + 1

Answer 1

Answer:

The velocity of the particle = -1.92 m/s

The speed of the particle = 5.72 m/s

Explanation:

Given equation of motion;

$f(t) = 18 \ + \ \frac{48}{t} \ + \ 1$

Velocity is defined as the change in displacement with time.

$V = \frac{df(t)}{dt} = -\frac{48}{t^2} \\\\at \ t = 5 \ s\\\\V = -\frac{48}{5^2} = \frac{-48}{25} = - 1.92 \ m/s$

The distance traveled by the particle in 5 s:

$s = f(5) = 18 + \frac{48}{5} + 1\\\\s= 28.6 \ m$

The speed of the particle when t = 5s

$Speed = \frac{28.6}{5} = 5.72 \ m/s$