Physics, 19.01.2020 14:31 tali2561

Adriver driving along a highway at a steady 45 mph (66 ft/sec) sees an accident ahead and slams on the brakes. what constant deceleration is required to stop the car in 242 ft? to find out, carry out the following steps. (1) solve the following initial value problem. startfraction d squared s over dt squared endfraction equals negative k (k constant), with startfraction ds over dt endfraction equals66 and sequals0 when tequals0 (2) find the value of t that makes startfraction ds over dt endfraction equals0. (the answer will involve k.) (3) find the value of k that makes sequals242 for the value of t found in the step (2).

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Answer from: nev322

9 ft/s²

Explanation:

d²s/dt² = -k

Integrate once:

ds/dt = -kt + C

At t=0, ds/dt = 66:

66 = -k(0) + C

C = 66

ds/dt = -kt + 66

Integrate again:

s = -½ kt² + 66t + D

At t=0, s = 0:

0 = -½ k (0)² + 66 (0) + D

D = 0

s = -½ kt² + 66t

Setting ds/dt = 0:

0 = -kt + 66

t = 66/k

Setting s = 242:

242 = -½ kt² + 66t

242 = -½ k (66/k)² + 66 (66/k)

242 = -2178/k + 4356/k

242 = 2178/k

k = 9

The driver must decelerate at 9 ft/s².

Answer from: Quest

the journeys of marquette, joliet and la salle a) new france expand.

all three of these explorers explored the midwest and the area around the great lakes, which they subsequently claimed for france.

this was a big portion of territory and expanded new france which before then only consisted of quebec province in northeastern canada

Answer from: Quest

m₁v₁ + m₂v₂ = (m₁ + m₂)vmomentum is conserved.the left-hand side of the equation represents the momentum in the system before the collision.the right-hand side represents the momentum in the system after the collisionm₁ and v₁ represents the mass and the velocity of the physics blockm₂ and v₂ represents the mass and velocity of the ball of puttyv represents the final velocity of the combined mass.the question states the two masses stick together. they combined mass has its own velocity with the body mass the sum of the two objects' massestheir combined momentum is (m₁ + m₂)vto find the magitude of (m₁ + m₂)v, we need to add the vectors on the left-hand side of the equation: m₁v₁ + m₂v₂.note the diagram. i have positioned the vectors in accordance with their directions.the magnitude of the resultant can be calculated using the pythagorean theorem since this is a right triangle situation (north and west are perpendicular)|(m₁ + m₂)v| = √[ (m₁v₁)² + (m₂v₂)² ]|(m₁ + m₂)v| = √[ (1.5kg·8.0m/s)² + (0.40kg·20m/s)² ]|(m₁ + m₂)v| = 14.4 kg m/sfor two significant figures (assuming that 20m/s is two), this rounds to 14 kg m/s

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Adriver driving along a highway at a steady 45 mph (66 ft/sec) sees an accident ahead and slams on t...