Mechanics | Relativity Answers

A startled armadillo leaps upward, rising 0.525 m in the first 0.215 s. (a) What is its initial speed as it leaves the ground? (b) What is its speed at the height of 0.525 m? (c) How much higher does it go?

You are arguing over a cell phone while trailing an unmarked police car by 26.0 m; both your car and the police car are traveling at 120 km/h. Your argument diverts your attention from the police car for 2.0 s (long enough for you to look at the phone and yell,“I won't do that!”). At the beginning of that 2.0 s, the police officer begins braking suddenly at 5.20 m/s^2. (a) What is the separation between the two cars when your attention finally returns? Suppose that you take another 0.500 s to realize your danger and begin braking. (b) If you too brake at 5.20 m/s^2, what is your speed when you hit the police car?

A car traveling 54.3 km/h is 24.3 m from a barrier when the driver slams on the brakes. The car hits the barrier 2.14 s later. (a) What is the car's constant deceleration magnitude before impact? (b) How fast is the car traveling at impact?

An electron has a constant acceleration of +2.9 m/s^2. At a certain instant its velocity is +8.7 m/s. What is its velocity (a) 1.6 s earlier and (b) 1.6 s later?

Catapulting mushrooms. Certain mushrooms launch their spores by a catapult mechanism. As water condenses from the air onto a spore that is attached to the mushroom, a drop grows on one side of the spore and a film grows on the other side. The spore is bent over by the drop's weight, but when the film reaches the drop, the drop's water suddenly spreads into the film and the spore springs upward so rapidly that it is slung off into the air. Typically, the spore reaches a speed of 1.70 m/s in a 5.40 μm launch; its speed is then reduced to zero in 1.20 mm by the air. Using that data and assuming constant accelerations, find the acceleration in terms of g during (a) the launch and (b) the speed reduction.

The position of a particle moving along the x axis depends on the time according to the equation x = ct^2 - bt^5, where x is in meters and t in seconds. Let c and b have numerical values 2.5 m/s^2 and 1.6 m/s^5, respectively. From t = 0.0 s to t = 1.3 s, (a) what is the displacement of the particle? Find its velocity at times (b) 1.0 s, (c) 2.0 s, (d) 3.0 s, and (e) 4.0 s. Find its acceleration at (f) 1.0 s, (g) 2.0 s, (h) 3.0 s, and (i) 4.0 s.

Two trains, each having a speed of 38 km/h, are headed at each other on the same straight track. A bird that can fly 76 km/h flies off the front of one train when they are 76 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 the bird travels?

Compute your average velocity in the following two cases: (a) You walk 88.0 m at a speed of 2.24 m/s and then run 88.0 m at a speed of 3.28 m/s along a straight track. (b) You walk for 1.00 min at a speed of 2.24 m/s and then run for 1.50 min at 3.28 m/s along a straight track.

Show that the angular momentum L=r×p vector is an axial vector.

A heavy solid sphere is thrown on a horizontal rough surface with initial velocity u without rolling. What will its speed be when it starts pure rolling motion?