The x and y coordinates of the particle at any time are x=5t−2t2 respectively where x and y are in meters and t in seconds. The acceleration of the particle at t=2s is
Question
The x and y coordinates of the particle at any time are x=5t−2t2 respectively where x and y are in meters and t in seconds. The acceleration of the particle at t=2s is
Solution
The given equations are for the position of the particle in the x and y directions. However, to find the acceleration, we need to find the second derivative of the position with respect to time, which gives us the acceleration.
The given equation is x = 5t - 2t^2.
First, let's find the velocity by taking the first derivative of the position with respect to time (t).
dx/dt = v = 5 - 4t
Now, let's find the acceleration by taking the second derivative of the position with respect to time (t), which is the first derivative of the velocity with respect to time.
d^2x/dt^2 = a = -4
The acceleration is constant and equal to -4 m/s^2. It does not depend on time, so the acceleration at t = 2s is also -4 m/s^2.
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