acceleration

1. Mechanics problem: ratios of velocities, times and distances

I am working through an old mechanics textbook for UK A-level (1970s/80s) and am having difficulty with following problem, which is from an old A-level paper. I have managed to solve the first part of the question, but am floundering on the second and third parts. Help please! This is the first...
2. velocity acceleration problem

The van travels over the hill described by y = (-0.0015x^2 + 15) ft. If it has a constant speed of 75 ft/s, determine the x and y components of the van's velocity and acceleration when x = 50 ft. This is what I found: v_y = -0.15v_x v = \sqrt{v_x^2 + v_y^2} v_x = 74.17 ft/s \leftarrow v_y =...
3. Determining whether acceleration is constant

Hi, I'm trying to solve for the following question: And the solutions is as follows: For the solution, I was basically able to reach line 3 until I did not how to simplify the expression any further. What I'm saying is that I don't really understand what the value of "v" within the...
4. uniform acceleration

A car, starting from rest and travelling from p to q on a straight level road, where | pq | = 10 000 m, reaches its maximum speed 25 m/s by constant acceleration in the first 500 m and continues at this maximum speed for the rest of the journey. A second car, starting from rest and travelling...
5. Displacement, velocity, acceleration and time question - Need to verify this

"The height above water of a life jacket dropped from a 4 m boat is given by the function: h(t) = (-2t + 4) / (t^2 + 1) where t is time in seconds after it is dropped and h is the height in meters above water. a) When does the life jacket reach a height of 1 m above water? b) For how long is...
6. Speed in a Clockwise Circle

A particle starting from rest revolves with uniformly increasing speed in a clockwise circle in the xy plane. The center of the circle is at the origin of an xy coordinate system. At t = 0, the particle is at x = 0, y = 2 m. At t = 2 s, it has made one-quarter of a revolution and is at x = 2 m...
7. Find Scalar Tangential/Normal Component of Acceleration Given Speed

Hello! I have two different questions, one asking for the scalar tangential component of acceleration and the other asking for the scalar normal component of acceleration, both given the speed, ||v||. I could really use some help with how to start solving these specific types of problems as my...
8. Vector Position, Acceleration, and Velocity

Find v(t) and r(t). Given a(t) = 7i + 8j v(0) = k r(0) = i v(t) = \int a(t) = \int 7i + 8j (dt) = 7ti + 8tj + k - makes sense. r(t) = \int v(t) = \int 7ti + 8tj + tk (dt) = (\dfrac{7t^{2}}{2} + 1)i + 4t^{2}j + tk ?? How did the + 1 come about?
9. Two Boxes - System Acceleration

There are two boxes of mass 10 kg. Box1 rests on a surface inclined at Θ to the horizontal, and it is connected to a lightweight cord, which passes over a massless and frictionless pulley, to Box2 which hangs freely. It is obvious that Box2 will fall and Box1 will rise up the plane with an...
10. Show that acceleration is always perpendicular to the radius vector

I need a little help on this problem: "A particle moves with radius vector $\vec r(t)=acos(\theta)\hat i +asin(\theta)\hat j+bcosh(\omega t)\hat k$ where $\omega$ is a constant and $\theta$ is a function of $t$: $\theta\equiv \theta (t)$. (a) Find the velocity $\dot r=\frac {d\vec r}{dt}$ at...
11. Acceleration question

Question : If the position of an object is given by a(t)=2t cos(t2), find the position function s(t) if v(0) = 0 and s(0)=0. Final answer should contain integral notation. My attempt (probably wrong): u= t^2 du/2 =tdt 1/2 integral cosu du 1/2 sinu+ c 1/2 sin (t^2) + c Would appreciate...
12. differentiation velocity, acceleration, displacement

1. A body moves with simple harmonic motion about an equilibrium point O. Its displacement from O, x metres, is related to time, t seconds, by: x=1.75 sin ((pi/4) t + 2.75) a) By differentiation find expressions for velocity and acceleration. b)...
13. Graph of velocity and acceleration. Which is which?

Please refer to the image for graph of the velocity and acceleration.
14. Time - Two Speeds

An unmarked police car traveling a constant 95 km/h is passed by a speeder traveling 140 km/h. Precisely 1 s after the speeder passes, the policeman steps on the accelerator; if the police car acceleration is 2 m/s^2, how much time passes before the police car overtakes the speeder (assumed...
15. GR Question #1: Acceleration

I have been working on what I thought would be a (reasonably) simple problem and I have found it to be completely intractable. The concept is simple enough...I wanted to let a rocket fall into a black hole while applying a constant acceleration of its own. But after problem after problem (I...
16. Finding the acceleration of a mass on a rough inclined slope.

Hi. Can someone please help me with these two pictures. I have tried everything I possibly could but I can't seem to be able to solve it. Thank You Very Much
17. Distance from acceleration

How can I find the distance car A passed? (without integration, in case it can be used here)
18. A Ball on Inclined Plane

A ball rolls down an inclined plane with an acceleration of 2 ft/sec^2. (a) If the ball is given no initial velocity, how far will it roll in t seconds? (b) What initial velocity must be given for the ball to roll 100 ft in 5 sec?
19. Average and Instantaneous Acceleration (physics)

Hey guys…I got an assignment from our physics class and I was having a hard time answering this problem (Crying) . Maybe if you could lend me some of your helps and of coarse it would mean a lot to me.(Handshake)(Bigsmile)(Smile)(Smile)(Kiss) Here’s the problem: “A test driver at incredible...
20. centripetal acceleration

Hello, Can someone please direct me along the right path to this question, I am really stuck. question is attached, I know the acceleration expression is (\ddot{r} - r \dot{\phi}^{2} )\hat{r} + ( 2\dot{r} \dot{\phi} + r \ddot{\phi} ) \hat{\phi} but am not sure how to put this together to...