Question

In a bicycle race Ram is travelling with constant velocity of 10m/s and is 15m ahead of Shyam. Shyam is travelling with a velocity of 8m/s with a acceleration of 2m/s^2. how much time elapses before Shyam overtakes ram?

Answer 1

Given:

In a bicycle race Ram is travelling with constant velocity of 10m/s and is 15m ahead of Shyam. Shyam is travelling with a velocity of 8m/s with a acceleration of 2m/s^2.

To find:

Time after which shyam overtakes Ram.

Calculation:

During the period of overtaking , the position of Ram and Shyam will be same.

So, in time t :

$\therefore \: d_{(shyam)} = 15 + d_{(ram)}$

$= > \: u_{(shyam)} t + \dfrac{1}{2}a {t}^{2} = 15 + (u_{ram} \times t)$

$= > \: 8t + \dfrac{1}{2}(2) {t}^{2} = 15 + (10\times t)$

$= > \: 8t + {t}^{2} = 15 + 10t$

$= > \: {t}^{2} - 2t - 15 = 0$

$= > \: {t}^{2} - (5 - 3)t - 15 = 0$

$= > \: {t}^{2} - 5t + 3t - 15 = 0$

$= > \: t(t - 5)+ 3(t - 5 )= 0$

$= > \: (t + 3)(t - 5 )= 0$

So, either t = -3 or +5

Considering positive value only , the time taken to overtake Ram is 5 seconds.

Hope It Helps.