Question

A particle with an initial velocity of 50 m slows at a constant acceleration to 20 ms-1 over a distance of 105 m. How long does it take for the particle to slow down? (a) 2 s (c) 3 s (b)4 s (d)5 s

Answer 1

Time taken, t = 3 s

Step-by-step explanation:

It is given that,

Initial velocity of the particle, u = 50 m/s

Final velocity, v = 20 m/s

Distance covered, s = 105 m

Firstly we will find the acceleration of the particle. It can be calculated using third equation of motion as :

`v^2-u^2=2as`

`a=(v^2-u^2)/(2s)`

`a=((20\ m/s)^2-(50\ m/s)^2)/(2* 105\ m)`

`a=-10\ m/s^2`

So, the particle is decelerating at the rate of 10 m/s². Let t is the time taken for the particle to slow down. Using first equation of motion as :

`t=(v-u)/(a)`

`t=(20\ m/s-50\ m/s)/(-10\ m/s^2)`

t = 3 s

So, the time taken for the particle to slow down is 3 s. Hence, this is the required solution.