Question

two particles are travelling along a straight line AB of length 20cm. at the same instant one particle starts from rest at A and travels towards B with a constant acceleration of 2m/s2 and the other particle starts form rest at Band travels towards A with a constant acceleration of 5m/s2. find how far from A the particles collide.

Answer 1

Answer on Question #48006, Physics, Mechanics | Kinematics | Dynamics

Two particles are travelling along a straight line AB of length 20cm. At the same instant one particle starts from rest at A and travels towards B with a constant acceleration of $2\mathrm{m}/\mathrm{s}^2$ and the other particle starts from rest at B and travels towards A with a constant acceleration of $5\mathrm{m}/\mathrm{s}^2$. Find how far from A the particles collide.

Solution:

The times of moving for two particles are the same.

$$t = \sqrt {\frac {2 d _ {1}}{a _ {1}}} = \sqrt {\frac {2 d _ {2}}{a _ {2}}}$$

where $d_1$ and $d_2$ are distances traveled.

Thus,

$$\frac {d _ {1}}{a _ {1}} = \frac {d _ {2}}{a _ {2}}$$ $$d _ {2} = d _ {1} \frac {a _ {2}}{a _ {1}}$$

The distance is

$$d _ {2} = L - d _ {1} = 2 0 \mathrm {c m} - \mathrm {d} _ {1}$$ $$L - d _ {1} = d _ {1} \frac {a _ {2}}{a _ {1}}$$ $$L = d _ {1} \left(1 + \frac {a _ {2}}{a _ {1}}\right)$$

So,

$$d _ {1} = \frac {L}{\left(1 + \frac {a _ {2}}{a _ {1}}\right)} = \frac {2 0}{1 + \frac {5}{2}} = \frac {4 0}{7} = 5. 7 \mathrm {c m}$$

Answer: $d_{1} = 5.7$ cm

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