Question

A particle is thrown vertically upward with initial velocity of 150m/s. Find the ratio of its speed at t=3s and t=5s. (Take g=10 $ms^{-2}$)

Answer 1

Let's consider the upward direction as positive.
The initial velocity of the particle, u = 150 $\frac{m}{s}$
Acceleration due to gravity, g = -10 $\frac{m}{s^2}$ (negative sign as it acts in the downward direction)
Using the kinematic equation, we can find the velocity of the particle at any time t as:
v = u - gt
At t = 3 s, the velocity of the particle is:
v1 = u - gt
= 150 - 10(3)
= 120 $\frac{m}{s}$
At t = 5 s, the velocity of the particle is:
v2 = u - gt
= 150 - 10(5)
= 100 $\frac{m}{s}$

Therefore, the ratio of the speed of the particle at t=3s to t=5s is:
$\frac{v_1}{v_2}$ = $\frac{120}{100}$ = $\frac{6}{5}$
$\therefore$ the ratio of the speed of the particle at t=3s to t=5s is 6:5. i.e 1.20