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Excel in math and science
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Displacement, Velocity, Acceleration
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Challenge Quizzes
As the elevator takes time to accelerate, and decelerate, the acceleration graph can be modeled as indicated in the above diagram.
Which of the following is the best graph to illustrate the velocity of the elevator?
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
A rocket starts at rest with acceleration at time \(t\) given by \(a(t)=\left(6t^2+10t\right) \text{ m/s}^2.\) What is its velocity (in \(\text{ m/s}\)) at \(t=10\) seconds?
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
The acceleration of a particle traveling in a straight line is given by the equation \(a(t)=2t.\) If the velocity at \(t=1\) is \(v=4\) and the distance from the starting point at \(t=1\) is \(s=15\), what is the distance from the starting point at \(t=2?\)
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
The acceleration of an object in motion is given by the vector \(\overrightarrow{a}(t)=(4t,e^t).\) If the object's initial velocity is \(\overrightarrow{v}(0)=(8,0),\) which of the following is the velocity vector as a function of time \(t?\)
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
The position of a particle at time \(t\) is given by vector \(<x,y>\) and its acceleration is given by \[\mathbf{a}=<-12\cos 2t, -7\sin t>\] for \(-\frac{\pi}{2} \leq t \leq \frac{\pi}{2}\). For \(t=0,\) the position vector of the particle is \(<3,0>\) with \(\displaystyle \frac{dx}{dt}=0\) and \(\displaystyle \frac{dy}{dx}=7.\) Find the position vector \(<x,y>\).