Question

The x and y coordinates of a particle at any time t are given by x=2t+4t 2 and y=5t, where x and y are in meter and t in second. The acceleration of the particle at t=5s is:

Answer 1

The acceleration of the particle at t=5s is 8 m/s² in the x-direction, as the acceleration in the y-direction is 0 m/s².

Step-by-step explanation:

The acceleration of a particle at any given time can be found by differentiating its velocity with respect to time. Given the position functions x=2t+4t2 and y=5t, we first need to find the velocity functions for both x and y by differentiating:

• Velocity in x-direction, vx(t) = dx/dt = d/dt(2t+4t2) = 2 + 8t
• Velocity in y-direction, vy(t) = dy/dt = d/dt(5t) = 5

To find the acceleration, we differentiate the velocity functions:

• Acceleration in x-direction, ax(t) = dvx/dt = d/dt(2 + 8t) = 8 m/s2
• Acceleration in y-direction, ay(t) = dvy/dt = d/dt(5) = 0 m/s2

At t=5s, the acceleration in the x-direction is 8 m/s2 and in the y-direction is 0 m/s2. Therefore, the total acceleration at t=5s is 8 m/s2 in the x-direction.