Helping with any of these would be extremely appreciated. An automobile travels

Question

Helping with any of these would be extremely appreciated.

An automobile travels on a straight road for 43 km at 49 km/h. It then continues in the same direction for another 43 km at 98 km/h. (a) What is the average velocity (in km/h) of the car during this 86 km trip? (Assume that it moves in the positive x direction.) (b) What is the average speed (in km/h)?

Two trains, each having a speed of 23 km/h, are headed at each other on the same straight track. A bird that can fly 46 km/h flies off the front of one train when they are 46 km apart and heads directly for the other train. On reaching the other train it flies directly back to the first train, and so forth. (We have no idea why a bird would behave in this way.) What is the total distance (in km) the bird travels?

A particle's position is given by x = 8.00 - 9.00t + 3t2, in which x is in meters and t is in seconds. (a) What is its velocity at t = 1 s? (b) Is it moving in the positive or negative direction of x just then? (c) What is its speed just then? (d) Is the speed increasing or decreasing just then? (Try answering the next two questions without further calculation.) (e) Is there ever an instant when the velocity is zero? If so, give the time t; if not, answer "0". (f) Is there a time after t = 3 s when the particle is moving in the negative direction of x? If so, give the time t; if not, answer "0".

At a certain time a particle had a speed of 59 m/s in the positive x direction, and 3.1 s later its speed was 84 m/s in the opposite direction. What was the average acceleration of the particle during this 3.1 s interval?

A hot-air balloon is ascending at the rate of 14 m/s and is 97 m above the ground when a package is dropped over the side. (a) How long does the package take to reach the ground? (b) With what speed does it hit the ground?

Explanation / Answer

1.

Note: velocity is speed + direction; speed is speed but no particular direction. Assume the driver is driving to the north

time@ 49 km/hr = 43/49 = 0.87755 hrs
time@ 98 km/hr = 43/98 = 0.438775 hrs

Total time: 1.3163 hrs; Total distance: 86 km

Average velocity: 86/1.3163 = 65.3346 km/hr in a +x direction Ans.

Average speed is the same i.e. 65.3346 km/hr , but no particular direction.

2. The total speed of the two trains is 46km/h toward each other, so they will take 46/46 hours, or 1.0 hours to collide.

During that time, the bird will have flown 46km/h x 1.00 hours = 46.0 km. Ans.

3. x = 8.00 - 9.00t + 3t2

v(t) = dx/dt = -9.0 + 6t

(a) velocity at t = 1 s   

v(t) = dx/dt = -9.0 + 6*1 = -3 m/sec Ans.

(b) The - sign represents Negative x direction

(c) speed is -3 m/sec Ans.

(d). speed is increasing as v(t) = dx/dt = -9.0 + 6t

(e) v(t) = dx/dt = -9.0 + 6t

velocity will be zero at 1.5 sec

f) after time t = 3 sec

v(t) = dx/dt = -9.0 + 6*3 = 9 m/sec

after that it will go in +x direction only. hence NO

4. we know that v = u + at

84 = 59 + a* 3.1

hence a = 8.064 m/sec2

5. b) we know that v^2 = u^2 + 2as

  v^2 = (-14)^2 + 2(9.8) (97)

v^2 = 196 + 2(9.8) (97)

so v = 45.79 m/s ans.

a) v = vo + gt

45.79 = -14 + 9.8 t

so t = (45.79 + 14) / 9.8 = 6.101 s ans.

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