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Two busses A and B are at positions 50m ...

Two busses A and B are at positions 50m and 100m from the origin at time t=0. They start moving in the same direction simultaneously wi8th uniform velocities of `10ms^(-1)` and `5ms^(-1)` . Determine the time and position at which A overtakes B.

Text Solution

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Here we use equation of motion for constant velocity in Cartesian form
Given `x_1(0)=50m,x_2(0)=100m`
`v_1=10ms^(-1),v_2=5ms^(-1)`
The positions of the two buses at any instant t are `x_1(t)=x_1(0)+v_1t=50+10t`
`x_2(t)=x_2(0)+v_2t=100+10t`
When A overtakes B,
`x_1(t)=x_2(t)`
`50+10t=100+5t` or `5t=50`
t=10s
`x_1(10)=x_2(10)=150m`
Thus A overtakes B at a position of 150 m from the origin at time t = 10 s.
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