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A particle of mass m moves from rest a time t=0, under the action of a variable force f(t) = A*t*exp(-B*t), where A,B are positive constants. Find the speed of the particle for large t, expressing the answer in terms of m, A, and B.

First, we need to find a formula for the speed of the particle, v, at a given time, t. Relate the speed, v, to the force f, using Newton's 2nd Law: f(t) = mdv/dt (remembering that acceleration is t...

Answered by Maths tutor
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How can you factorise expressions with power 3 or higher?

The key to factoring big and complicated expressions into simpler forms is to remember the factor theorem. The factor theorem says that if we plug a number k into our expression ...

Answered by Christopher D. Maths tutor
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Prove by contradiction that there is an infinite number of prime numbers.

The 'by contradiction' tells us we need to assume the opposite to begin with: 1) Let's assume there is a finite number of prime numbers2) Let P be the largest prime number (the last one) 3) if we multiply...

Answered by Charlotte L. Maths tutor
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What are the necessary conditions for a random variable to have a binomial distribution?

There can only be two possible outcomes, 'success' and 'fail' (e.g heads or tails) There is a fixed number of trialsThe probabilities of 'success' and 'fail' are constant and stay the same in each trial (...

Answered by Julie T. Maths tutor
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Solve the quadratic equation x^2 + x - 6 = 0

There are 3 methods for solving quadratic equations;FactorisingThe quadratic equationCompleting the SquareUsing method 1,We observe that 2 and 3 are factors of 6 and that 3 - 2 = 1 so by factoring out we ...

Answered by Thomas A. Maths tutor
2901 Views

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