# Set of 5 problems on kinematics

1) A car covers one-quarter of the distance to the next town at 40km/h, another quarter at 50 km/h and the rest at 90km/h. Find the car's average speed for the entire distance.

2) In order to qualify for the finals in a racing event, a race car must achieve an average speed of 250km/h on a track with a total length of 1600m. If a particular car covers the first half of the track at an average speed of 230 km/h, what minimum average speed must it have in the second half of the track in order to qualify?

3) Two cars travel in the same direction along a straight highway, one at a constant speed of 55mi/h and the other at 70mi/h. a) Assuming that they start at the same point, how much sooner does the faster car arrive at a destination 10 miles away? b) How far must the faster car travel before it has a 15-min lead on the slower car?

4) An object with an initial velocity 8m/s moves along a straight line with constant acceleration and travels 640m in 40s. For the 40-s interval, find a) the average velocity and b) the final velocity and c) the acceleration of the object.

5) Just as a car accelerates from rest with an acceleration of 1.4m/s2, a bus moving with a constant speed of 12m/s passes in a parallel lane in the same direction. a) How long does the car take to overtake the bus? b) How fast the car then be going? c) How far will the car then have traveled?

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Problems on kinematics and dynamics

6.) An airplane flies due south with respect to the ground at an air speed of 900 km/h for 2.0 hr before turning and moving southwest with respect to the ground for 3.0 hr. During the entire trip, a wind blows in the easterly direction at 120 km/h. (a) What is the plane's average speed with respect to the ground? (b) What is the plane's average velocity with respect to the ground? (c) What is the final position vector?

7.) Five forces, all of the same magnitude F, act on an object of mass m at the origin of the coordinate system. Two of the forces are aligned along the x-axis; one is oriented in the +x direction and one in the -x direction. Two other forces are similarly aligned with the z-axis. The fifth force points int he +y direction. What are the direction and magnitude of the acceleraation of the object? If we had specified the forces in a different order, would the answer have been different?

8.) A father pulls his identical twins on identical sleds tied one after the other. He exerts a force F that makes an angle of 30 degrees with the horizontal and that leads to an acceleration of the two sleds. What is the tension in the rope that he is pulling? What is the tension in the rope that connects the front sled to the rear sled? The mass of each sled plus its twin is m. Assume that there is no friction between the sleds runners and the snow surface.

9.) A force of magnitude 8.0 N pushes on a horizontally stacked set of blocks on a frictionless surface with masses m1 = 2.0 kg, m2 = 3.0 kg, m3 = 4.0 kg. (a) What is the acceleration of the stack? (b) What are the forces on block 1 as well as the net force on this block? (c) Repeat part b for block 2. (d) Repeat part b for block 3.

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