Two cars with speeds v1 and v2 are headed toward one another along a straight le

Question

Two cars with speeds v1 and v2 are headed toward one another along a straight level road. When they are in the distance d apart, each driver sees the others car and applies brakes. Assuming both cars have equal magnitude accelerations a after the brakes are applied, derive an algebraic formula for the minimum distance d which avoid collision in terms of v1 v2 and a Two cars with speeds v1 and v2 are headed toward one another along a straight level road. When they are in the distance d apart, each driver sees the others car and applies brakes. Assuming both cars have equal magnitude accelerations a after the brakes are applied, derive an algebraic formula for the minimum distance d which avoid collision in terms of v1 v2 and a

Explanation / Answer

For first car.

to find distance traveled by it to stop from v1 using,

vf^2 - vi^2 = 2 a d

0^2 - v1^2 =2 (-a)d1

d1 = v1^2 /2a

For second car.

to find distance traveled by it to stop from v2 using,

vf^2 - vi^2 = 2 a d

0^2 - v2^2 =2 (-a)d2

d2 = v2^2 /2a

minimum distance required between them = d1 +d2 = v1^2/ 2a + v2^2 /2a = (v1^2 + v2^2) / 2a

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.