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Simple Harmonic Motion is a specific type of periodic motion where is any motion whose displacement-time equation, apart from the constants, is a single sine and/or cosine function. Of particular importance is a certain kind of rectilinear motion known as Simple Harmonic Motion. A particle is said to be undergoing in simple harmonic motion with […]
Projectile motion on an inclined plane is one variation of projectile motion and the trajectory can be used to determine the position of the landing object on the included plane. We will discuss; path of the trajectory of the projectile range of the projectile maximum range initial direction is perpendicular to the direction at which […]
$$ \begin{align} a &= \displaystyle \frac{d}{dx} \left( \frac{1}{2} v^2 \right) \\ v &= \frac{dx}{dt} \end{align} $$ Example A particle is moving so that the acceleration \( a = 32x^3 + 48 x^2 + 16x \). Initially \( x=1 \) and \( v=-8 \). Part 1 Show that \( \displaystyle a = \frac{d}{dx} \left( \frac{1}{2}v^2 \right) […]
A particle is moving in a straight line, starting from the origin. At time t seconds the particle has a displacement of x metres from the origin and a velocity v. The displacement is described as a logarithmic expression in terms of time t. Find an expression for v, the initial velocity, when the particle comes to rest and the distance travelled by the particle in the first three seconds.
Example 1 Find the maximum value of $i=100\sin(50 \pi t +0.32)$, and the time when this maximum occurs. \( \begin{align} \displaystyle \dfrac{di}{dt} &= 0 \\ 100\cos(50 \pi t+ 0.32) \times 50 \pi &= 0 \\ \cos(50 \pi t+ 0.32) &= 0 \\ 50 \pi t+ 0.32 &= \dfrac{\pi}{2}, \dfrac{3\pi}{2}, \cdots \\ t &= \dfrac{1}{50 \pi}\Big(\dfrac{\pi}{2}-0.32\Big), […]
Collision of Projectile Motion is handled by setting the same vertical height and horizontal distance at a given time. Worked Examples of Collision of Projectile Motion Two Points \(A\) and \(B\) are \(d\) metres apart. A particle is projected from \(A\) towards \(B\) with initial velocity \(u\) m/s at angle \( \alpha \) to the […]