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Two cars, A and B move along the x-axis....

Two cars, `A` and `B` move along the x-axis. Car `A` starts from rest with constant accelertion while car `B` moves with consstant velocity.
a. At what time `s`, t `s`, if any, do `A` and `B` have the same position?
.
b. At what time `s` if any, do `A` and `B` have the same velocity? What is the velocity of car `B` at this time.
c. Graph velocity versus time for both `A` and `B`.
d. At what time `s`. If any, does car `A pass car `A`?
e. At what time `s`, if any does car `B` pass car `A`?

Text Solution

Verified by Experts

The two cars have the same position at time when when their `x-t` graphs cross. The firure shows this occurs at `t=1 s` and `t=3 s`.
b. `A` and `B` have the same velpcoty when slpe of the tangent on parabola is equal to the slope of the straight line.From position-time graph, it is clear it occurs at `t=2 s`.
Car `B` travels with constant velocitly.
`v_(B)=(20-0)/(4-0) =5 ms^(-1)`
c.
d. Car `A` passes car `B` when`x_(A)` moves above `x_(B)` in the `x-t` graph
This happens at `t=3 s`
e. Car `B` passes car `A` when `x_(B)` moves above `x_(A)`, x-t graph.
This happens at `t= 1 s`.
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