**Problem1**:

While traveling along a straight interstate highway you notice that the mile marker reads 260. You travel until you reach the 150-mile marker, and then retrace your path to the 175-mile marker. What is the magnitude of your resultant displacement from the 260-mile marker?

- Solution:

The resultant displacement is the vector**d**, the sum of two vectors**d**_{1}and**d**_{2}which point in opposite directions. The magnitude of the resultant displacement vector is (260 - 175) miles = 85 miles.

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**Problem2:**

In a time interval of 5 minutes, a runner runs once around a one-mile track. What is his average velocity? What is his average speed?- Solution:

After 5 minute the runner returns to his starting position. The displacement is zero, so his average velocity is zero.

The**average speed**is the distance traveled in the time interval Dt. This distance is one mile. The average speed therefore is (1 mile)/(5 minutes) = (12 miles)/(60 minutes) = 12 miles/h.**Note:**Speed is a scalar, velocity is a vector.**The average speed is in general not equal to the magnitude of the average velocity**.

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**Problem3:**

A motorist drives north for 35 minutes at 85 km/h and then stops for 15 minutes. He then continues north, traveling 130 km in 2 hours.(a) What is his total displacement?

(b) What is his average velocity?

- Solution:

(a) In the first 35 minutes the motorist travels

d_{1 }= v_{1}t_{1 }= 85 km/h ´ 35 min ´ 1 h/(60 min) = 49.6 km.

In the next 2 hours he travels 130 km. The total distance traveled is 179.6 km. His displacement is 179.6 km (north).

(b) His average velocity is**v**=**d**/t. He travels for 170 minutes (including his stop). Therefore his average velocity is= (179.6 km/(170 min)) ´ (60 min/h) (north) = 63.4 km/h (north).

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