1. A car travels up a hill at a constant speed of 15 km/h and returns down the h

Question

1. A car travels up a hill at a constant speed of 15 km/h and returns down the hill at a constant speed of 47 km/h. Calculate the average speed for the round trip.

2. In 1 km races, runner 1 on track 1 (with time 2 min, 27.97 s) appears to be faster than runner 2 on track 2 (2 min, 28.49 s). However, the length L2 of track 2 might be slightly greater than the length L1 of track 1. How large can L2 L1 be for us still to conclude that runner 1 is faster?

3. An electron moving along the x axis has a position given by x = 18te3t m, where t is in seconds. How far is the electron from the origin when it momentarily stops?

4. The position function x(t) of a particle moving along an x axis is x = 3.9 5.1t2, with x in meters and t in seconds.

(a) At what time does the particle (momentarily) stop?

(b) Where does the particle (momentarily) stop?

(c) At what negative time does the particle pass through the origin?

(d) At what positive time does the particle pass through the origin?

(e) Graph x versus t for the range 5 s to +5 s.

(f) To shift the curve rightward on the graph, should we include the term 20t or the term +20t in x(t)?

20t? 20t?      

(g) Does that inclusion increase or decrease the value of x at which the particle momentarily stops?

increase? decrease?   

5. The position of a particle moving along the x axis is given in centimeters by x = 6.50 + 3.50t3, where t is in seconds. Consider the time interval t = 2.00 s to t = 3.00 s. (Indicate the direction with the sign of your answer.)

(a) Calculate the average velocity.
cm/s

(b) Calculate the instantaneous velocity at t = 2.00 s.
cm/s

(c) Calculate the instantaneous velocity at t = 3.00 s.
cm/s

(d) Calculate the instantaneous velocity at t = 2.50 s.
cm/s

(e) Calculate the instantaneous velocity when the particle is midway between its positions at t = 2.00 s and t = 3.00 s.
cm/s

(f) Graph x versus t and indicate your answers graphically.

6. The position of a particle moving along an x axis is given by x = 17t2 3t3, where x is in meters and t is in seconds.

(a) Determine the position of the particle at t = 3.0 s.
m

(b) Determine the velocity of the particle at t = 3.0 s. (Indicate the direction with the sign of your answer.)
m/s

(c) Determine the acceleration of the particle at t = 3.0 s. (Indicate the direction with the sign of your answer.)
m/s2

(d) What is the maximum positive coordinate reached by the particle?
m

(e) At what time is it reached?
s

(f) What is the maximum positive velocity reached by the particle?
m/s

(g) At what time is it reached?
s

(h) What is the acceleration of the particle at the instant the particle is not moving (other than at t = 0)? (Indicate the direction with the sign of your answer.)
m/s2

(i) Determine the average velocity of the particle between t = 0 and t = 3 s. (Indicate the direction with the sign of your answer.)
m/s

7. At a certain time a particle had a speed of 15 m/s in the positive x direction, and 2.8 s later its speed was 31 m/s in the opposite direction. What is the average acceleration of the particle during this 2.8 s interval?

direction?

8. An electron with initial velocity v0 = 1.30 105 m/s enters a region 1.0 cm long where it is electrically accelerated. It emerges with velocity v = 5.30 106 m/s. What was its acceleration, assumed constant? (Such a process occurs in old-fashioned television sets.)
m/s2

9. (a) If the maximum acceleration that is tolerable for passengers in a subway train is 1.78 m/s2 and subway stations are located 750 m apart, what is the maximum speed a subway train can attain between stations?
m/s

(b) What is the travel time between stations?
s

(c) If a subway train stops for 15 s at each station, what is the maximum average speed of the train, from one start-up to the next?
m/s

(d) Graph x, v, and a versus t for the interval from one start-up to the next.

10. A startled armadillo leaps upward rising 0.549 m in the first 0.191 s.

(a) What is its initial speed as it leaves the ground? (Enter your answer to at least two decimal places.)
m/s

(b) What is its speed at the height of 0.549 m?
m/s

(c) How much higher does it go?
m

Explanation / Answer

1. A car travels up a hill at a constant speed of 15 km/h and returns down the hill at a constant speed of 47 km/h. Calculate the average speed for the round trip.

Let's say distance = x km
Time taken during uphill = x/15
Time taken during downhill = x/47

Total time taken, = (x/15 + x/47)
Total distance = 2x

Average speed, = Total distance / Total time taken
Average speed, = 2x / (x/15 + x/47)
Average speed, = 22.74 km/hr
Average speed for the round trip, = 22.74 km/hr

(2)
In 1 km races, runner 1 on track 1 (with time 2 min, 27.97 s) appears to be faster than runner 2 on track 2 (2 min, 28.49 s). However, the length L2 of track 2 might be slightly greater than the length L1 of track 1. How large can L2 L1 be for us still to conclude that runner 1 is faster?

Let the speed of runner 1 be v1
Let the speed of runner 2 be v2

Speed = Distance / time
For runner 1 to be faster, v1 > v2
L1/(120 + 27.97) > L2/(120 + 28.49)
L1 > L2 * (120 + 27.97) / (120 + 28.49)
L1 > L2 * 0.996
L2 = 1.0035 L1

So L2 - L1 = 0.0035 Km OR 3.5 m

please post separate questions in separate post only

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