# 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...