Question

a particle moves along the x-axis. it is position as a function of time is given by x=6,8t+8,5t^2 , where t is in seconds and x is in meters . what is the acceleration as a function of time ?

Answer 1

Answer:

17 m/s²

Explanation:

A particle moves along the x-axis. Its position as a function of time is given by x = 6.8 t + 8.5 t²

where t is in seconds and x is in meters.

The first derivative of x is the object's velocity.

f'(x) = v = 6.8 + 2 × 8.5 t = 6.8 + 17 t

The second derivative of x is the acceleration.

f''(x) = a = 17

The acceleration of the particle is 17 m/s².

Answer 2

To answer this question you simply need to consider the definition of acceleration which, for one-dimensional motion, is simply $a \equiv \frac{d^2 x}{dt^2}$. So take your second derivative and you are done!